Theorem neldifsnd

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

	Ref	Expression
Assertion	neldifsnd	⊢ ( 𝜑 → ¬ 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } ) )

Proof

Step	Hyp	Ref	Expression
1		neldifsn	⊢ ¬ 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } )
2	1	a1i	⊢ ( 𝜑 → ¬ 𝐴 ∈ ( 𝐵 ∖ { 𝐴 } ) )