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Metamath Proof Explorer

Theorem relin1

Description: The intersection with a relation is a relation. (Contributed by NM, 16-Aug-1994)

		Ref	Expression
	Assertion	relin1	$⊢ Rel A \to Rel (A \cap B)$

Step	Hyp	Ref	Expression
1		inss1	$⊢ A \cap B \subseteq A$
2		relss	$⊢ A \cap B \subseteq A \to (Rel A \to Rel (A \cap B))$
3	1 2	ax-mp	$⊢ Rel A \to Rel (A \cap B)$