Theorem neldifsn

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

	Ref	Expression
Assertion	neldifsn	⊢ ¬ 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } )

Proof

Step	Hyp	Ref	Expression
1		neirr	⊢ ¬ 𝐴 ≠ 𝐴
2		eldifsni	⊢ ( 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } ) → 𝐴 ≠ 𝐴 )
3	1 2	mto	⊢ ¬ 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } )