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Metamath Proof Explorer

Theorem dfdif2

Description: Alternate definition of class difference. (Contributed by NM, 25-Mar-2004)

		Ref	Expression
	Assertion	dfdif2	$⊢ A ∖ B = \{x \in A \| \neg x \in B\}$

Step	Hyp	Ref	Expression
1		df-dif	$⊢ A ∖ B = \{x \| (x \in A \land \neg x \in B)\}$
2		df-rab	$⊢ \{x \in A \| \neg x \in B\} = \{x \| (x \in A \land \neg x \in B)\}$
3	1 2	eqtr4i	$⊢ A ∖ B = \{x \in A \| \neg x \in B\}$