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

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 ) )

Proof

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 ) )