Theorem afv2eq2 42066

Description: Equality theorem for function value, analogous to fveq2 6412. (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 2801	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 22	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afv2eq12d 42064	1 ⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

Syntax hints:   → wi 4   = wceq 1653  ''''cafv2 42057

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2378  ax-ext 2778

This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2787  df-cleq 2793  df-clel 2796  df-nfc 2931  df-rex 3096  df-rab 3099  df-v 3388  df-dif 3773  df-un 3775  df-in 3777  df-ss 3784  df-nul 4117  df-if 4279  df-pw 4352  df-sn 4370  df-pr 4372  df-op 4376  df-uni 4630  df-br 4845  df-opab 4907  df-xp 5319  df-rel 5320  df-cnv 5321  df-co 5322  df-dm 5323  df-rn 5324  df-res 5325  df-iota 6065  df-fun 6104  df-dfat 41968  df-afv2 42058

This theorem is referenced by: (None)