Theorem fveq12d

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

	Ref	Expression
Hypotheses	fveq12d.1	$$⊢\phi \to F=G$$
	fveq12d.2	$$⊢\phi \to A=B$$
Assertion	fveq12d	$$⊢\phi \to F\left(A\right)=G\left(B\right)$$

Proof

Step	Hyp	Ref	Expression
1		fveq12d.1	$$⊢\phi \to F=G$$
2		fveq12d.2	$$⊢\phi \to A=B$$
3	1	fveq1d	$$⊢\phi \to F\left(A\right)=G\left(A\right)$$
4	2	fveq2d	$$⊢\phi \to G\left(A\right)=G\left(B\right)$$
5	3 4	eqtrd	$$⊢\phi \to F\left(A\right)=G\left(B\right)$$