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Mirrors > Home > MPE Home > Th. List > curf12 | Unicode version |
Description: The partially evaluated curry functor at a morphism. (Contributed by Mario Carneiro, 12-Jan-2017.) |
Ref | Expression |
---|---|
curfval.g |
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curfval.a |
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curfval.c |
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curfval.d |
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curfval.f |
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curfval.b |
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curf1.x |
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curf1.k |
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curf11.y |
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curf12.j |
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curf12.1 |
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curf12.y |
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curf12.g |
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Ref | Expression |
---|---|
curf12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | curfval.g |
. . . 4
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2 | curfval.a |
. . . 4
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3 | curfval.c |
. . . 4
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4 | curfval.d |
. . . 4
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5 | curfval.f |
. . . 4
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6 | curfval.b |
. . . 4
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7 | curf1.x |
. . . 4
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8 | curf1.k |
. . . 4
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9 | curf12.j |
. . . 4
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10 | curf12.1 |
. . . 4
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11 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 | curf1 14285 |
. . 3
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12 | fvex 5709 |
. . . . . 6
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13 | 6, 12 | eqeltri 2482 |
. . . . 5
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14 | 13 | mptex 5933 |
. . . 4
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15 | 13, 13 | mpt2ex 6392 |
. . . 4
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16 | 14, 15 | op2ndd 6325 |
. . 3
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17 | 11, 16 | syl 16 |
. 2
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18 | curf11.y |
. . 3
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19 | curf12.y |
. . . 4
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20 | 19 | adantr 452 |
. . 3
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21 | ovex 6073 |
. . . . 5
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22 | 21 | mptex 5933 |
. . . 4
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23 | 22 | a1i 11 |
. . 3
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24 | curf12.g |
. . . . . 6
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25 | 24 | adantr 452 |
. . . . 5
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26 | simprl 733 |
. . . . . 6
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27 | simprr 734 |
. . . . . 6
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28 | 26, 27 | oveq12d 6066 |
. . . . 5
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29 | 25, 28 | eleqtrrd 2489 |
. . . 4
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30 | ovex 6073 |
. . . . 5
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31 | 30 | a1i 11 |
. . . 4
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32 | simplrl 737 |
. . . . . . 7
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33 | 32 | opeq2d 3959 |
. . . . . 6
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34 | simplrr 738 |
. . . . . . 7
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35 | 34 | opeq2d 3959 |
. . . . . 6
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36 | 33, 35 | oveq12d 6066 |
. . . . 5
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37 | eqidd 2413 |
. . . . 5
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38 | simpr 448 |
. . . . 5
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39 | 36, 37, 38 | oveq123d 6069 |
. . . 4
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40 | 29, 31, 39 | fvmptdv2 5785 |
. . 3
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41 | 18, 20, 23, 40 | ovmpt2dv 6173 |
. 2
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42 | 17, 41 | mpd 15 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: curf1cl 14288 curf2cl 14291 uncfcurf 14299 diag12 14304 yon12 14325 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 ax-rep 4288 ax-sep 4298 ax-nul 4306 ax-pow 4345 ax-pr 4371 ax-un 4668 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2266 df-mo 2267 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-ne 2577 df-ral 2679 df-rex 2680 df-reu 2681 df-rab 2683 df-v 2926 df-sbc 3130 df-csb 3220 df-dif 3291 df-un 3293 df-in 3295 df-ss 3302 df-nul 3597 df-if 3708 df-pw 3769 df-sn 3788 df-pr 3789 df-op 3791 df-uni 3984 df-iun 4063 df-br 4181 df-opab 4235 df-mpt 4236 df-id 4466 df-xp 4851 df-rel 4852 df-cnv 4853 df-co 4854 df-dm 4855 df-rn 4856 df-res 4857 df-ima 4858 df-iota 5385 df-fun 5423 df-fn 5424 df-f 5425 df-f1 5426 df-fo 5427 df-f1o 5428 df-fv 5429 df-ov 6051 df-oprab 6052 df-mpt2 6053 df-1st 6316 df-2nd 6317 df-curf 14274 |
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