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Metamath Proof Explorer

Theorem neqne

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

Ref Expression
Assertion neqne ( ¬ 𝐴 = 𝐵 → 𝐴 ≠ 𝐵 )

Proof

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