Theorem fveq1d

Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003)

	Ref	Expression
Hypothesis	fveq1d.1	⊢ ( 𝜑 → 𝐹 = 𝐺 )
Assertion	fveq1d	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		fveq1d.1	⊢ ( 𝜑 → 𝐹 = 𝐺 )
2		fveq1	⊢ ( 𝐹 = 𝐺 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) )