Theorem fveq2

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

	Ref	Expression
Assertion	fveq2	$$⊢A=B\to F\left(A\right)=F\left(B\right)$$

Proof

Step	Hyp	Ref	Expression
1		breq1	$$⊢A=B\to \left(AFx\leftrightarrow BFx\right)$$
2	1	iotabidv	$$⊢A=B\to \left(\iota x|AFx\right)=\left(\iota x|BFx\right)$$
3		df-fv	$$⊢F\left(A\right)=\left(\iota x|AFx\right)$$
4		df-fv	$$⊢F\left(B\right)=\left(\iota x|BFx\right)$$
5	2 3 4	3eqtr4g	$$⊢A=B\to F\left(A\right)=F\left(B\right)$$