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Metamath Proof Explorer

Theorem disjdif

Description: A class and its relative complement are disjoint. Theorem 38 of Suppes p. 29. (Contributed by NM, 24-Mar-1998)

		Ref	Expression
	Assertion	disjdif	$⊢ A \cap (B ∖ A) = \emptyset$

Step	Hyp	Ref	Expression
1		inss1	$⊢ A \cap B \subseteq A$
2		inssdif0	$⊢ A \cap B \subseteq A \leftrightarrow A \cap (B ∖ A) = \emptyset$
3	1 2	mpbi	$⊢ A \cap (B ∖ A) = \emptyset$