Theorem opelxp1

Description: The first member of an ordered pair of classes in a Cartesian product belongs to first Cartesian product argument. (Contributed by NM, 28-May-2008) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	opelxp1	$$⊢⟨A,B⟩\in \left(C\times D\right)\to A\in C$$

Proof

Step	Hyp	Ref	Expression
1		opelxp	$$⊢⟨A,B⟩\in \left(C\times D\right)\leftrightarrow \left(A\in C\wedge B\in D\right)$$
2	1	simplbi	$$⊢⟨A,B⟩\in \left(C\times D\right)\to A\in C$$