Theorem fveq12d

Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008)

	Ref	Expression
Hypotheses	fveq12d.1	⊢ ( 𝜑 → 𝐹 = 𝐺 )
	fveq12d.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	fveq12d	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		fveq12d.1	⊢ ( 𝜑 → 𝐹 = 𝐺 )
2		fveq12d.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3	1	fveq1d	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) )
4	2	fveq2d	⊢ ( 𝜑 → ( 𝐺 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 ) )
5	3 4	eqtrd	⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 ) )