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Metamath Proof Explorer

Theorem opelvv

Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by NM, 22-Aug-2013) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Hypotheses	opelvv.1	$⊢ A \in V$
	opelvv.2	$⊢ B \in V$
Assertion	opelvv	$⊢ ⟨A, B⟩ \in (V \times V)$

Proof

Step	Hyp	Ref	Expression
1		opelvv.1	$⊢ A \in V$
2		opelvv.2	$⊢ B \in V$
3		opelxpi	$⊢ (A \in V \land B \in V) \to ⟨A, B⟩ \in (V \times V)$
4	1 2 3	mp2an	$⊢ ⟨A, B⟩ \in (V \times V)$