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Metamath Proof Explorer

Theorem brinxp

Description: Intersection of binary relation with Cartesian product. (Contributed by NM, 9-Mar-1997)

		Ref	Expression
	Assertion	brinxp	$⊢ (A \in C \land B \in D) \to (A R B \leftrightarrow A (R \cap (C \times D)) B)$

Step	Hyp	Ref	Expression
1		brinxp2	$⊢ A (R \cap (C \times D)) B \leftrightarrow ((A \in C \land B \in D) \land A R B)$
2	1	baibr	$⊢ (A \in C \land B \in D) \to (A R B \leftrightarrow A (R \cap (C \times D)) B)$