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Theorem fvex 5087
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 A 𝑊
Assertion
Ref Expression
fvex (𝐹A) V

Proof of Theorem fvex
StepHypRef Expression
1 fvex.1 . 2 𝐹 𝑉
2 fvex.2 . 2 A 𝑊
3 fvexg 5086 . 2 ((𝐹 𝑉 A 𝑊) → (𝐹A) V)
41, 2, 3mp2an 404 1 (𝐹A) V
Colors of variables: wff set class
Syntax hints:   wcel 1375  Vcvv 2533  cfv 4796
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 1315  ax-7 1316  ax-gen 1317  ax-ie1 1362  ax-ie2 1363  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-13 1386  ax-14 1387  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411  ax-ext 2004  ax-sep 3827  ax-pow 3879  ax-pr 3896  ax-un 4093
This theorem depends on definitions:  df-bi 110  df-3an 877  df-tru 1231  df-nf 1329  df-sb 1628  df-eu 1884  df-mo 1885  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2287  df-rex 2288  df-v 2535  df-un 2900  df-in 2902  df-ss 2909  df-pw 3313  df-sn 3333  df-pr 3334  df-op 3336  df-uni 3533  df-br 3717  df-opab 3771  df-cnv 4246  df-dm 4248  df-rn 4249  df-iota 4761  df-fv 4804
This theorem is referenced by:  rdgruledefgg  5847
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