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Theorem afveq2 32459
Description: Equality theorem for function value, analogous to fveq1 5847. (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 2455 . 2  |-  ( A  =  B  ->  F  =  F )
2 id 22 . 2  |-  ( A  =  B  ->  A  =  B )
31, 2afveq12d 32457 1  |-  ( A  =  B  ->  ( F''' A )  =  ( F''' B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1398  '''cafv 32438
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-uni 4236  df-br 4440  df-opab 4498  df-xp 4994  df-rel 4995  df-cnv 4996  df-co 4997  df-dm 4998  df-res 5000  df-iota 5534  df-fun 5572  df-fv 5578  df-dfat 32440  df-afv 32441
This theorem is referenced by:  ffnaov  32523
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