Theorem opelxpd

Description: Ordered pair membership in a Cartesian product, deduction form. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Hypotheses	opelxpd.1	|- ( ph -> A e. C )
	opelxpd.2	|- ( ph -> B e. D )
Assertion	opelxpd	|- ( ph -> <. A , B >. e. ( C X. D ) )

Proof

Step	Hyp	Ref	Expression
1		opelxpd.1	|- ( ph -> A e. C )
2		opelxpd.2	|- ( ph -> B e. D )
3		opelxpi	|- ( ( A e. C /\ B e. D ) -> <. A , B >. e. ( C X. D ) )
4	1 2 3	syl2anc	|- ( ph -> <. A , B >. e. ( C X. D ) )