This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem inss1

Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of TakeutiZaring p. 18. (Contributed by NM, 27-Apr-1994)

		Ref	Expression
	Assertion	inss1	$⊢ A \cap B \subseteq A$

Proof

Step	Hyp	Ref	Expression
1		elinel1	$⊢ x \in (A \cap B) \to x \in A$
2	1	ssriv	$⊢ A \cap B \subseteq A$