This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ecased

Description: Deduction for elimination by cases. (Contributed by NM, 8-Oct-2012)

Ref Expression
Hypotheses ecased.1 ⊢ φ → ¬ ψ → θ
ecased.2 ⊢ φ → ¬ χ → θ
ecased.3 ⊢ φ → ψ ∧ χ → θ
Assertion ecased ⊢ φ → θ

Proof

Step Hyp Ref Expression
1 ecased.1 ⊢ φ → ¬ ψ → θ
2 ecased.2 ⊢ φ → ¬ χ → θ
3 ecased.3 ⊢ φ → ψ ∧ χ → θ
4 pm3.11 ⊢ ¬ ¬ ψ ∨ ¬ χ → ψ ∧ χ
5 4 3 syl5 ⊢ φ → ¬ ¬ ψ ∨ ¬ χ → θ
6 1 2 5 ecase3d ⊢ φ → θ