Metamath Proof Explorer


Theorem neqne

Description: From non-equality to inequality. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Assertion neqne ( ¬ 𝐴 = 𝐵𝐴𝐵 )

Proof

Step Hyp Ref Expression
1 id ( ¬ 𝐴 = 𝐵 → ¬ 𝐴 = 𝐵 )
2 1 neqned ( ¬ 𝐴 = 𝐵𝐴𝐵 )