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Theorem afveq2 27668
Description: Equality theorem for function value, analogous to fveq1 5667. (Contributed by Alexander van der Vekens, 22-Jul-2017.)
Assertion
Ref Expression
afveq2  |-  ( A  =  B  ->  ( F''' A )  =  ( F''' B ) )

Proof of Theorem afveq2
StepHypRef Expression
1 eqidd 2388 . 2  |-  ( A  =  B  ->  F  =  F )
2 id 20 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2afveq12d 27666 1  |-  ( A  =  B  ->  ( F''' A )  =  ( F''' B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649  '''cafv 27640
This theorem is referenced by:  ffnaov  27732
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-opab 4208  df-xp 4824  df-rel 4825  df-cnv 4826  df-co 4827  df-dm 4828  df-res 4830  df-iota 5358  df-fun 5396  df-fv 5402  df-dfat 27642  df-afv 27643
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