Theorem opelxp2

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

	Ref	Expression
Assertion	opelxp2	$$⊢⟨A,B⟩\in \left(C\times D\right)\to B\in D$$

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	simprbi	$$⊢⟨A,B⟩\in \left(C\times D\right)\to B\in D$$