Metamath Proof Explorer


Theorem pm2.61i

Description: Inference eliminating an antecedent. (Contributed by NM, 5-Apr-1994) (Proof shortened by Wolf Lammen, 19-Nov-2023)

Ref Expression
Hypotheses pm2.61i.1 ⊢ φ → ψ
pm2.61i.2 ⊢ ¬ φ → ψ
Assertion pm2.61i ⊢ ψ

Proof

Step Hyp Ref Expression
1 pm2.61i.1 ⊢ φ → ψ
2 pm2.61i.2 ⊢ ¬ φ → ψ
3 1 2 nsyl4 ⊢ ¬ ψ → ψ
4 3 pm2.18i ⊢ ψ