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 ) )