Theorem afv2eq2 48031

Description: Equality theorem for function value, analogous to fveq2 6885. (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 2766	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 23	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	afv2eq12d 48029	1 ⊢ (𝐴 = 𝐵 → (𝐹''''𝐴) = (𝐹''''𝐵))

This proof depends on syntax axioms:   → wi 4   = wceq 1570  ''''cafv2 48022

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-rab 3419  df-v 3459  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4287  df-if 4490  df-pw 4566  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4875  df-br 5112  df-opab 5176  df-xp 5669  df-rel 5670  df-cnv 5671  df-co 5672  df-dm 5673  df-rn 5674  df-res 5675  df-iota 6496  df-fun 6542  df-dfat 47933  df-afv2 48023

This theorem is used by: (None)