Theorem afv2eq2 44660

Description: Equality theorem for function value, analogous to fveq2 6768. (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 2740	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afv2eq12d 44658	1 ⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

Syntax hints:   → wi 4   = wceq 1541  ''''cafv2 44651

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1544  df-fal 1554  df-ex 1786  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-rab 3074  df-v 3432  df-dif 3894  df-un 3896  df-in 3898  df-ss 3908  df-nul 4262  df-if 4465  df-pw 4540  df-sn 4567  df-pr 4569  df-op 4573  df-uni 4845  df-br 5079  df-opab 5141  df-xp 5594  df-rel 5595  df-cnv 5596  df-co 5597  df-dm 5598  df-rn 5599  df-res 5600  df-iota 6388  df-fun 6432  df-dfat 44562  df-afv2 44652

This theorem is referenced by: (None)