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Metamath Proof Explorer

Theorem orim12i

Description: Disjoin antecedents and consequents of two premises. (Contributed by NM, 6-Jun-1994) (Proof shortened by Wolf Lammen, 25-Jul-2012)

Ref Expression
Hypotheses orim12i.1 ⊢ ( 𝜑 → 𝜓 )
orim12i.2 ⊢ ( 𝜒 → 𝜃 )
Assertion orim12i ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) )

Proof

Step Hyp Ref Expression
1 orim12i.1 ⊢ ( 𝜑 → 𝜓 )
2 orim12i.2 ⊢ ( 𝜒 → 𝜃 )
3 1 orcd ⊢ ( 𝜑 → ( 𝜓 ∨ 𝜃 ) )
4 2 olcd ⊢ ( 𝜒 → ( 𝜓 ∨ 𝜃 ) )
5 3 4 jaoi ⊢ ( ( 𝜑 ∨ 𝜒 ) → ( 𝜓 ∨ 𝜃 ) )