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Theorem afv2eq1 45914
Description: Equality theorem for function value, analogous to fveq1 6890. (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 2733 . 2 (𝐹 = 𝐺𝐴 = 𝐴)
31, 2afv2eq12d 45913 1 (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  ''''cafv2 45906
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-pw 4604  df-sn 4629  df-pr 4631  df-op 4635  df-uni 4909  df-br 5149  df-opab 5211  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-dm 5686  df-rn 5687  df-res 5688  df-iota 6495  df-fun 6545  df-dfat 45817  df-afv2 45907
This theorem is referenced by: (None)
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