Theorem afv2eq2

Description: Equality theorem for function value, analogous to fveq2 . (Contributed by AV, 4-Sep-2022)

	Ref	Expression
Assertion	afv2eq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 '''' 𝐴 ) = ( 𝐹 '''' 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		eqidd	⊢ ( 𝐴 = 𝐵 → 𝐹 = 𝐹 )
2		id	⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
3	1 2	afv2eq12d	⊢ ( 𝐴 = 𝐵 → ( 𝐹 '''' 𝐴 ) = ( 𝐹 '''' 𝐵 ) )