Theorem afv2eq2 43773

Description: Equality theorem for function value, analogous to fveq2 6645. (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 2799	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afv2eq12d 43771	1 ⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

Syntax hints:   → wi 4   = wceq 1538  ''''cafv2 43764

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770

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 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-rab 3115  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-if 4426  df-pw 4499  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-opab 5093  df-xp 5525  df-rel 5526  df-cnv 5527  df-co 5528  df-dm 5529  df-rn 5530  df-res 5531  df-iota 6283  df-fun 6326  df-dfat 43675  df-afv2 43765

This theorem is referenced by: (None)