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Theorem afveq1 27147
Description: Equality theorem for function value, analogous to fveq1 5562. (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 19 . 2  |-  ( F  =  G  ->  F  =  G )
2 eqidd 2317 . 2  |-  ( F  =  G  ->  A  =  A )
31, 2afveq12d 27146 1  |-  ( F  =  G  ->  ( F''' A )  =  ( G''' A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1633  '''cafv 27120
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-rex 2583  df-rab 2586  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-uni 3865  df-br 4061  df-opab 4115  df-xp 4732  df-rel 4733  df-cnv 4734  df-co 4735  df-dm 4736  df-res 4738  df-iota 5256  df-fun 5294  df-fv 5300  df-dfat 27122  df-afv 27123
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