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Theorem afveq2 30190
Description: Equality theorem for function value, analogous to fveq1 5799. (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 30188 1  |-  ( A  =  B  ->  ( F''' A )  =  ( F''' B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370  '''cafv 30167
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-xp 4955  df-rel 4956  df-cnv 4957  df-co 4958  df-dm 4959  df-res 4961  df-iota 5490  df-fun 5529  df-fv 5535  df-dfat 30169  df-afv 30170
This theorem is referenced by:  ffnaov  30254
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