Theorem afv2eq1 47981

Description: Equality theorem for function value, analogous to fveq1 6880. (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 23	. 2 ⊢ (𝐹 = 𝐺 → 𝐹 = 𝐺)
2		eqidd 2764	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	afv2eq12d 47980	1 ⊢ (𝐹 = 𝐺 → (𝐹''''𝐴) = (𝐺''''𝐴))

This proof depends on syntax axioms:   → wi 4   = wceq 1570  ''''cafv2 47973

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4488  df-pw 4564  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-opab 5174  df-xp 5667  df-rel 5668  df-cnv 5669  df-co 5670  df-dm 5671  df-rn 5672  df-res 5673  df-iota 6492  df-fun 6538  df-dfat 47884  df-afv2 47974

This theorem is used by: (None)