Metamath Proof Explorer

Theorem jaod

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 18-Aug-1994)

Ref Expression
Hypotheses jaod.1 φ ψ χ
jaod.2 φ θ χ
Assertion jaod φ ψ θ χ


Step Hyp Ref Expression
1 jaod.1 φ ψ χ
2 jaod.2 φ θ χ
3 1 com12 ψ φ χ
4 2 com12 θ φ χ
5 3 4 jaoi ψ θ φ χ
6 5 com12 φ ψ θ χ