Theorem neldifsn

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

	Ref	Expression
Assertion	neldifsn	$$⊢\neg A\in \left(B\setminus \left\{A\right\}\right)$$

Proof

Step	Hyp	Ref	Expression
1		neirr	$$⊢\neg A\ne A$$
2		eldifsni	$$⊢A\in \left(B\setminus \left\{A\right\}\right)\to A\ne A$$
3	1 2	mto	$$⊢\neg A\in \left(B\setminus \left\{A\right\}\right)$$