Theorem fnop

Description: The first argument of an ordered pair in a function belongs to the function's domain. (Contributed by NM, 8-Aug-1994)

	Ref	Expression
Assertion	fnop	$$⊢\left(FFnA\wedge ⟨B,C⟩\in F\right)\to B\in A$$

Proof

Step	Hyp	Ref	Expression
1		df-br	$$⊢BFC\leftrightarrow ⟨B,C⟩\in F$$
2		fnbr	$$⊢\left(FFnA\wedge BFC\right)\to B\in A$$
3	1 2	sylan2br	$$⊢\left(FFnA\wedge ⟨B,C⟩\in F\right)\to B\in A$$