Metamath Proof Explorer


Theorem neneq

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

Ref Expression
Assertion neneq ⊢ A ≠ B → ¬ A = B

Proof

Step Hyp Ref Expression
1 id ⊢ A ≠ B → A ≠ B
2 1 neneqd ⊢ A ≠ B → ¬ A = B