Theorem fveqeq2

Description: Equality deduction for function value. (Contributed by BJ, 31-Aug-2022)

	Ref	Expression
Assertion	fveqeq2	⊢ ( 𝐴 = 𝐵 → ( ( 𝐹 ‘ 𝐴 ) = 𝐶 ↔ ( 𝐹 ‘ 𝐵 ) = 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
2	1	fveqeq2d	⊢ ( 𝐴 = 𝐵 → ( ( 𝐹 ‘ 𝐴 ) = 𝐶 ↔ ( 𝐹 ‘ 𝐵 ) = 𝐶 ) )