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Metamath Proof Explorer

Theorem pm2.24ii

Description: A contradiction implies anything. Inference associated with pm2.21i and pm2.24i . (Contributed by NM, 27-Feb-2008)

Ref Expression
Hypotheses pm2.24ii.1 ⊢ φ
pm2.24ii.2 ⊢ ¬ φ
Assertion pm2.24ii ⊢ ψ

Proof

Step Hyp Ref Expression
1 pm2.24ii.1 ⊢ φ
2 pm2.24ii.2 ⊢ ¬ φ
3 2 pm2.21i ⊢ φ → ψ
4 1 3 ax-mp ⊢ ψ