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Mirrors > Home > MPE Home > Th. List > funssfv | Structured 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 5803 |
. . . 4
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2 | 1 | eqcomd 2459 |
. . 3
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3 | funssres 5556 |
. . . 4
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4 | 3 | fveq1d 5791 |
. . 3
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5 | 2, 4 | sylan9eqr 2514 |
. 2
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6 | 5 | 3impa 1183 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4511 ax-nul 4519 ax-pr 4629 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3070 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-sn 3976 df-pr 3978 df-op 3982 df-uni 4190 df-br 4391 df-opab 4449 df-id 4734 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-res 4950 df-iota 5479 df-fun 5518 df-fv 5524 |
This theorem is referenced by: funsssuppss 6815 tfrlem9 6944 tfrlem11 6947 ac6sfi 7657 axdc3lem2 8721 axdc3lem4 8723 imasvscaval 14578 pserdv 22010 eupap1 23732 sspn 24269 subfacp1lem2a 27202 subfacp1lem2b 27203 subfacp1lem5 27206 cvmliftlem10 27317 cvmliftlem13 27319 wfrlem12 27869 wfrlem14 27871 frrlem11 27914 bnj945 32067 bnj1502 32141 bnj545 32188 bnj548 32190 |
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