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Metamath Proof Explorer

Theorem inex2g

Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g . (Contributed by Peter Mazsa, 19-Dec-2018)

		Ref	Expression
	Assertion	inex2g	$⊢ A \in V \to B \cap A \in V$

Step	Hyp	Ref	Expression
1		incom	$⊢ B \cap A = A \cap B$
2		inex1g	$⊢ A \in V \to A \cap B \in V$
3	1 2	eqeltrid	$⊢ A \in V \to B \cap A \in V$