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Metamath Proof Explorer

Theorem disjdifr

Description: A class and its relative complement are disjoint. (Contributed by Thierry Arnoux, 29-Nov-2023)

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

Step	Hyp	Ref	Expression
1		incom	$⊢ A \cap (B ∖ A) = (B ∖ A) \cap A$
2		disjdif	$⊢ A \cap (B ∖ A) = \emptyset$
3	1 2	eqtr3i	$⊢ (B ∖ A) \cap A = \emptyset$