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Metamath Proof Explorer

Theorem jaodan

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 14-Oct-2005)

Ref Expression
Hypotheses jaodan.1 ⊢ φ ∧ ψ → χ
jaodan.2 ⊢ φ ∧ θ → χ
Assertion jaodan ⊢ φ ∧ ψ ∨ θ → χ

Proof

Step Hyp Ref Expression
1 jaodan.1 ⊢ φ ∧ ψ → χ
2 jaodan.2 ⊢ φ ∧ θ → χ
3 1 ex ⊢ φ → ψ → χ
4 2 ex ⊢ φ → θ → χ
5 3 4 jaod ⊢ φ → ψ ∨ θ → χ
6 5 imp ⊢ φ ∧ ψ ∨ θ → χ