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Mirrors > Home > MPE Home > Th. List > ovmpt2ga | Unicode version |
Description: Value of an operation given by a maps-to rule. (Contributed by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ovmpt2ga.1 |
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ovmpt2ga.2 |
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Ref | Expression |
---|---|
ovmpt2ga |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2924 |
. 2
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2 | ovmpt2ga.2 |
. . . 4
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3 | 2 | a1i 11 |
. . 3
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4 | ovmpt2ga.1 |
. . . 4
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5 | 4 | adantl 453 |
. . 3
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6 | simp1 957 |
. . 3
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7 | simp2 958 |
. . 3
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8 | simp3 959 |
. . 3
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9 | 3, 5, 6, 7, 8 | ovmpt2d 6160 |
. 2
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10 | 1, 9 | syl3an3 1219 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: ovmpt2a 6163 ovmpt2g 6167 elovmpt2 6250 offval 6271 offval3 6277 bropopvvv 6385 hashbcval 13325 setsvalg 13447 ressval 13471 restval 13609 sylow1lem4 15190 sylow3lem2 15217 sylow3lem3 15218 lsmvalx 15228 mvrfval 16439 opsrval 16490 cnmpt12 17652 cnmpt22 17659 qtopval 17680 flimval 17948 fclsval 17993 ucnval 18260 stdbdmetval 18497 wlkon 21483 trlon 21493 pthon 21528 spthon 21535 ofcfval3 24438 fmulcl 27578 is2wlkonot 28060 is2spthonot 28061 2wlkonot 28062 2spthonot 28063 2wlksot 28064 2spthsot 28065 2wlkonot3v 28072 2spthonot3v 28073 |
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-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-sep 4290 ax-nul 4298 ax-pr 4363 |
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 2258 df-mo 2259 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-sbc 3122 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-uni 3976 df-br 4173 df-opab 4227 df-id 4458 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-iota 5377 df-fun 5415 df-fv 5421 df-ov 6043 df-oprab 6044 df-mpt2 6045 |
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