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Theorem afveq1 27974
Description: Equality theorem for function value, analogous to fveq1 5727. (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 20 . 2  |-  ( F  =  G  ->  F  =  G )
2 eqidd 2437 . 2  |-  ( F  =  G  ->  A  =  A )
31, 2afveq12d 27973 1  |-  ( F  =  G  ->  ( F''' A )  =  ( G''' A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652  '''cafv 27948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-res 4890  df-iota 5418  df-fun 5456  df-fv 5462  df-dfat 27950  df-afv 27951
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