Theorem fveq12i

Description: Equality deduction for function value. (Contributed by FL, 27-Jun-2014)

	Ref	Expression
Hypotheses	fveq12i.1	⊢ 𝐹 = 𝐺
	fveq12i.2	⊢ 𝐴 = 𝐵
Assertion	fveq12i	⊢ ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fveq12i.1	⊢ 𝐹 = 𝐺
2		fveq12i.2	⊢ 𝐴 = 𝐵
3	1	fveq1i	⊢ ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 )
4	2	fveq2i	⊢ ( 𝐺 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 )
5	3 4	eqtri	⊢ ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐵 )