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Metamath Proof Explorer

Theorem mpjaod

Description: Eliminate a disjunction in a deduction. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses jaod.1 ⊢ φ → ψ → χ
jaod.2 ⊢ φ → θ → χ
jaod.3 ⊢ φ → ψ ∨ θ
Assertion mpjaod ⊢ φ → χ

Proof

Step Hyp Ref Expression
1 jaod.1 ⊢ φ → ψ → χ
2 jaod.2 ⊢ φ → θ → χ
3 jaod.3 ⊢ φ → ψ ∨ θ
4 1 2 jaod ⊢ φ → ψ ∨ θ → χ
5 3 4 mpd ⊢ φ → χ