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Theorem fvex 5120
Description: Evaluating a set function at a set exists. (Contributed by Mario Carneiro and Jim Kingdon, 28-May-2019.)
Hypotheses
Ref Expression
fvex.1  F  V
fvex.2  W
Assertion
Ref Expression
fvex  F `

_V

Proof of Theorem fvex
StepHypRef Expression
1 fvex.1 . 2  F  V
2 fvex.2 . 2  W
3 fvexg 5119 . 2  F  V  W  F `  _V
41, 2, 3mp2an 404 1  F `

_V
Colors of variables: wff set class
Syntax hints:   wcel 1374   _Vcvv 2535   ` cfv 4829
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-sep 3849  ax-pow 3901  ax-pr 3918  ax-un 4120
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-nf 1330  df-sb 1628  df-eu 1885  df-mo 1886  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289  df-rex 2290  df-v 2537  df-un 2899  df-in 2901  df-ss 2908  df-pw 3336  df-sn 3356  df-pr 3357  df-op 3359  df-uni 3555  df-br 3739  df-opab 3793  df-cnv 4280  df-dm 4282  df-rn 4283  df-iota 4794  df-fv 4837
This theorem is referenced by:  rdgruledefgg  5882
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