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Metamath Proof Explorer

Theorem 0in

Description: The intersection of the empty set with a class is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020)

		Ref	Expression
	Assertion	0in	$⊢ \emptyset \cap A = \emptyset$

Step	Hyp	Ref	Expression
1		incom	$⊢ \emptyset \cap A = A \cap \emptyset$
2		in0	$⊢ A \cap \emptyset = \emptyset$
3	1 2	eqtri	$⊢ \emptyset \cap A = \emptyset$