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Theorem afveq1 32424
Description: Equality theorem for function value, analogous to fveq1 5790. (Contributed by Alexander van der Vekens, 22-Jul-2017.)
Assertion
Ref Expression
afveq1  |-  ( F  =  G  ->  ( F''' A )  =  ( G''' A ) )

Proof of Theorem afveq1
StepHypRef Expression
1 id 22 . 2  |-  ( F  =  G  ->  F  =  G )
2 eqidd 2397 . 2  |-  ( F  =  G  ->  A  =  A )
31, 2afveq12d 32423 1  |-  ( F  =  G  ->  ( F''' A )  =  ( G''' A ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1399  '''cafv 32404
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1633  ax-4 1646  ax-5 1719  ax-6 1765  ax-7 1808  ax-10 1855  ax-11 1860  ax-12 1872  ax-13 2020  ax-ext 2374
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1402  df-ex 1628  df-nf 1632  df-sb 1758  df-clab 2382  df-cleq 2388  df-clel 2391  df-nfc 2546  df-rex 2752  df-rab 2755  df-v 3053  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3729  df-if 3875  df-sn 3962  df-pr 3964  df-op 3968  df-uni 4181  df-br 4385  df-opab 4443  df-xp 4936  df-rel 4937  df-cnv 4938  df-co 4939  df-dm 4940  df-res 4942  df-iota 5477  df-fun 5515  df-fv 5521  df-dfat 32406  df-afv 32407
This theorem is referenced by: (None)
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