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 )