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Metamath Proof Explorer

Theorem neldifsn

Description: The class A is not in ( B \ { A } ) . (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Assertion	neldifsn	$⊢ \neg A \in (B ∖ \{A\})$

Step	Hyp	Ref	Expression
1		neirr	$⊢ \neg A \neq A$
2		eldifsni	$⊢ A \in (B ∖ \{A\}) \to A \neq A$
3	1 2	mto	$⊢ \neg A \in (B ∖ \{A\})$