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Metamath Proof Explorer

Theorem pm2.21fal

Description: If a wff and its negation are provable, then falsum is provable. (Contributed by Mario Carneiro, 9-Feb-2017)

Ref Expression
Hypotheses pm2.21fal.1 ⊢ ( 𝜑 → 𝜓 )
pm2.21fal.2 ⊢ ( 𝜑 → ¬ 𝜓 )
Assertion pm2.21fal ( 𝜑 → ⊥ )

Proof

Step Hyp Ref Expression
1 pm2.21fal.1 ⊢ ( 𝜑 → 𝜓 )
2 pm2.21fal.2 ⊢ ( 𝜑 → ¬ 𝜓 )
3 1 2 pm2.21dd ⊢ ( 𝜑 → ⊥ )