Theorem afv2eq1 46477

Description: Equality theorem for function value, analogous to fveq1 6883. (Contributed by AV, 4-Sep-2022.)

Assertion

Ref	Expression
afv2eq1	⊢ (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

Proof of Theorem afv2eq1

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝐹 = 𝐺 → 𝐹 = 𝐺)
2		eqidd 2727	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	afv2eq12d 46476	1 ⊢ (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

Syntax hints:   → wi 4   = wceq 1533  ''''cafv2 46469

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-pw 4599  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-xp 5675  df-rel 5676  df-cnv 5677  df-co 5678  df-dm 5679  df-rn 5680  df-res 5681  df-iota 6488  df-fun 6538  df-dfat 46380  df-afv2 46470

This theorem is referenced by: (None)