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Metamath Proof Explorer

Theorem ecase3

Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 26-Nov-2012)

Ref Expression
Hypotheses ecase3.1 ⊢ φ → χ
ecase3.2 ⊢ ψ → χ
ecase3.3 ⊢ ¬ φ ∨ ψ → χ
Assertion ecase3 ⊢ χ

Proof

Step Hyp Ref Expression
1 ecase3.1 ⊢ φ → χ
2 ecase3.2 ⊢ ψ → χ
3 ecase3.3 ⊢ ¬ φ ∨ ψ → χ
4 1 2 jaoi ⊢ φ ∨ ψ → χ
5 4 3 pm2.61i ⊢ χ