Theorem afv2eq1 47121

Description: Equality theorem for function value, analogous to fveq1 6914. (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 2741	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	afv2eq12d 47120	1 ⊢ (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

Syntax hints:   → wi 4   = wceq 1537  ''''cafv2 47113

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-in 3983  df-ss 3993  df-nul 4353  df-if 4549  df-pw 4624  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-opab 5229  df-xp 5701  df-rel 5702  df-cnv 5703  df-co 5704  df-dm 5705  df-rn 5706  df-res 5707  df-iota 6520  df-fun 6570  df-dfat 47024  df-afv2 47114

This theorem is referenced by: (None)