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Metamath Proof Explorer

Theorem neii

Description: Inference associated with df-ne . (Contributed by BJ, 7-Jul-2018)

Ref Expression
Hypothesis neii.1 ⊢ 𝐴 ≠ 𝐵
Assertion neii ¬ 𝐴 = 𝐵

Proof

Step Hyp Ref Expression
1 neii.1 ⊢ 𝐴 ≠ 𝐵
2 df-ne ⊢ ( 𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵 )
3 1 2 mpbi ⊢ ¬ 𝐴 = 𝐵