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Mirrors > Home > MPE Home > Th. List > funssfv | Structured version Visualization version Unicode version |
Description: The value of a member of the domain of a subclass of a function. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
funssfv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvres 5884 |
. . . 4
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2 | 1 | eqcomd 2459 |
. . 3
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3 | funssres 5625 |
. . . 4
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4 | 3 | fveq1d 5872 |
. . 3
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5 | 2, 4 | sylan9eqr 2509 |
. 2
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6 | 5 | 3impa 1204 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pr 4642 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-rab 2748 df-v 3049 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-sn 3971 df-pr 3973 df-op 3977 df-uni 4202 df-br 4406 df-opab 4465 df-id 4752 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-res 4849 df-iota 5549 df-fun 5587 df-fv 5593 |
This theorem is referenced by: funsssuppss 6946 wfrlem12 7052 wfrlem14 7054 tfrlem9 7108 tfrlem11 7111 ac6sfi 7820 axdc3lem2 8886 axdc3lem4 8888 imasvscaval 15456 pserdv 23396 eupap1 25716 sspn 26387 bnj945 29597 bnj1502 29671 bnj545 29718 bnj548 29720 subfacp1lem2a 29915 subfacp1lem2b 29916 subfacp1lem5 29919 cvmliftlem10 30029 cvmliftlem13 30031 frrlem11 30538 subgruhgredgd 39366 subumgredg2 39367 subupgr 39369 |
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