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Metamath Proof Explorer

Theorem inss2

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	inss2	$⊢ A \cap B \subseteq B$

Proof

Step	Hyp	Ref	Expression
1		incom	$⊢ B \cap A = A \cap B$
2		inss1	$⊢ B \cap A \subseteq B$
3	1 2	eqsstrri	$⊢ A \cap B \subseteq B$