Theorem fveq2d

Description: Equality deduction for function value. (Contributed by NM, 29-May-1999)

	Ref	Expression
Hypothesis	fveq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	fveq2d	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		fveq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		fveq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) )