Theorem afv2eq2 47117

Description: Equality theorem for function value, analogous to fveq2 6901. (Contributed by AV, 4-Sep-2022.)

Assertion

Ref	Expression
afv2eq2	⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

Proof of Theorem afv2eq2

Step	Hyp	Ref	Expression
1		eqidd 2734	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afv2eq12d 47115	1 ⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

Syntax hints:   → wi 4   = wceq 1535  ''''cafv2 47108

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1087  df-tru 1538  df-fal 1548  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-rab 3433  df-v 3479  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4531  df-pw 4606  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4915  df-br 5150  df-opab 5212  df-xp 5689  df-rel 5690  df-cnv 5691  df-co 5692  df-dm 5693  df-rn 5694  df-res 5695  df-iota 6510  df-fun 6560  df-dfat 47019  df-afv2 47109

This theorem is referenced by: (None)