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 ¬ 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 } )