Theorem fveq1

Description: Equality theorem for function value. (Contributed by NM, 29-Dec-1996)

	Ref	Expression
Assertion	fveq1	$$⊢F=G\to F\left(A\right)=G\left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		breq	$$⊢F=G\to \left(AFx\leftrightarrow AGx\right)$$
2	1	iotabidv	$$⊢F=G\to \left(\iota x|AFx\right)=\left(\iota x|AGx\right)$$
3		df-fv	$$⊢F\left(A\right)=\left(\iota x|AFx\right)$$
4		df-fv	$$⊢G\left(A\right)=\left(\iota x|AGx\right)$$
5	2 3 4	3eqtr4g	$$⊢F=G\to F\left(A\right)=G\left(A\right)$$