Theorem afv2eq1 46598

Description: Equality theorem for function value, analogous to fveq1 6899. (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 2728	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	afv2eq12d 46597	1 ⊢ (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

Syntax hints:   → wi 4   = wceq 1533  ''''cafv2 46590

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 2698

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-pw 4606  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-opab 5213  df-xp 5686  df-rel 5687  df-cnv 5688  df-co 5689  df-dm 5690  df-rn 5691  df-res 5692  df-iota 6503  df-fun 6553  df-dfat 46501  df-afv2 46591

This theorem is referenced by: (None)