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Metamath Proof Explorer

Theorem pm2.01i

Description: Inference associated with the weak Clavius law pm2.01 . (Contributed by BJ, 30-Mar-2020)

Ref Expression
Hypothesis pm2.01i.1 ⊢ ( 𝜑 → ¬ 𝜑 )
Assertion pm2.01i ¬ 𝜑

Proof

Step Hyp Ref Expression
1 pm2.01i.1 ⊢ ( 𝜑 → ¬ 𝜑 )
2 pm2.01 ⊢ ( ( 𝜑 → ¬ 𝜑 ) → ¬ 𝜑 )
3 1 2 ax-mp ⊢ ¬ 𝜑