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Theorem afv2eq1 43702
Description: Equality theorem for function value, analogous to fveq1 6660. (Contributed by AV, 4-Sep-2022.)
Assertion
Ref Expression
afv2eq1 (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

Proof of Theorem afv2eq1
StepHypRef Expression
1 id 22 . 2 (𝐹 = 𝐺𝐹 = 𝐺)
2 eqidd 2825 . 2 (𝐹 = 𝐺𝐴 = 𝐴)
31, 2afv2eq12d 43701 1 (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  ''''cafv2 43694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3142  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-if 4451  df-pw 4524  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-opab 5115  df-xp 5548  df-rel 5549  df-cnv 5550  df-co 5551  df-dm 5552  df-rn 5553  df-res 5554  df-iota 6302  df-fun 6345  df-dfat 43605  df-afv2 43695
This theorem is referenced by: (None)
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