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Metamath Proof Explorer

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

Proof

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