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Metamath Proof Explorer

Theorem disj2

Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 17-May-1998)

		Ref	Expression
	Assertion	disj2	$⊢ A \cap B = \emptyset \leftrightarrow A \subseteq V ∖ B$

Step	Hyp	Ref	Expression
1		ssv	$⊢ A \subseteq V$
2		reldisj	$⊢ A \subseteq V \to (A \cap B = \emptyset \leftrightarrow A \subseteq V ∖ B)$
3	1 2	ax-mp	$⊢ A \cap B = \emptyset \leftrightarrow A \subseteq V ∖ B$