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Mirrors > Home > ILE Home > Th. List > fvexg | Unicode version |
Description: Evaluating a set function at a set exists. (Contributed by Mario Carneiro and Jim Kingdon, 28-May-2019.) |
Ref | Expression |
---|---|
fvexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2748 |
. . 3
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2 | fvssunirng 5525 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | rnexg 4887 |
. . 3
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5 | uniexg 4435 |
. . 3
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6 | 4, 5 | syl 14 |
. 2
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7 | ssexg 4139 |
. 2
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8 | 3, 6, 7 | syl2anr 290 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-cnv 4630 df-dm 4632 df-rn 4633 df-iota 5173 df-fv 5219 |
This theorem is referenced by: fvex 5530 ovexg 5902 rdgivallem 6375 frecabex 6392 mapsnconst 6687 cc2lem 7243 addvalex 7821 uzennn 10409 absval 10981 climmpt 11279 strnfvnd 12452 grpsubval 12796 mulgval 12862 mulgfng 12863 iscnp4 13351 cnpnei 13352 |
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