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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > funimass4f | Unicode version |
Description: Membership relation for the values of a function whose image is a subclass. (Contributed by Thierry Arnoux, 24-Apr-2017.) |
Ref | Expression |
---|---|
funimass4f.1 |
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funimass4f.2 |
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funimass4f.3 |
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Ref | Expression |
---|---|
funimass4f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funimass4f.3 |
. . . . . 6
![]() ![]() ![]() ![]() | |
2 | 1 | nffun 5439 |
. . . . 5
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3 | funimass4f.1 |
. . . . . 6
![]() ![]() ![]() ![]() | |
4 | 1 | nfdm 5074 |
. . . . . 6
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5 | 3, 4 | nfss 3305 |
. . . . 5
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6 | 2, 5 | nfan 1842 |
. . . 4
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7 | 1, 3 | nfima 5174 |
. . . . 5
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8 | funimass4f.2 |
. . . . 5
![]() ![]() ![]() ![]() | |
9 | 7, 8 | nfss 3305 |
. . . 4
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10 | 6, 9 | nfan 1842 |
. . 3
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11 | funfvima2 5937 |
. . . 4
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12 | ssel 3306 |
. . . 4
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13 | 11, 12 | sylan9 639 |
. . 3
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14 | 10, 13 | ralrimi 2751 |
. 2
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15 | 3, 1 | dfimafnf 24000 |
. . . 4
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16 | 15 | adantr 452 |
. . 3
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17 | 8 | abrexss 23950 |
. . . 4
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18 | 17 | adantl 453 |
. . 3
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19 | 16, 18 | eqsstrd 3346 |
. 2
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20 | 14, 19 | impbida 806 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: ballotlem7 24750 |
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 2389 ax-sep 4294 ax-nul 4302 ax-pr 4367 |
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 2262 df-mo 2263 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-ne 2573 df-ral 2675 df-rex 2676 df-rab 2679 df-v 2922 df-sbc 3126 df-dif 3287 df-un 3289 df-in 3291 df-ss 3298 df-nul 3593 df-if 3704 df-sn 3784 df-pr 3785 df-op 3787 df-uni 3980 df-br 4177 df-opab 4231 df-id 4462 df-xp 4847 df-rel 4848 df-cnv 4849 df-co 4850 df-dm 4851 df-rn 4852 df-res 4853 df-ima 4854 df-iota 5381 df-fun 5419 df-fn 5420 df-fv 5425 |
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