Theorem fveqeq2d

Description: Equality deduction for function value. (Contributed by BJ, 30-Aug-2022)

	Ref	Expression
Hypothesis	fveqeq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	fveqeq2d	⊢ ( 𝜑 → ( ( 𝐹 ‘ 𝐴 ) = 𝐶 ↔ ( 𝐹 ‘ 𝐵 ) = 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		fveqeq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2	1	fveq2d	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) )
3	2	eqeq1d	⊢ ( 𝜑 → ( ( 𝐹 ‘ 𝐴 ) = 𝐶 ↔ ( 𝐹 ‘ 𝐵 ) = 𝐶 ) )