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	$$⊢\phi \to \psi$$
	orim12i.2	$$⊢\chi \to \theta$$
Assertion	orim12i	$$⊢\left(\phi \vee \chi \right)\to \left(\psi \vee \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		orim12i.1	$$⊢\phi \to \psi$$
2		orim12i.2	$$⊢\chi \to \theta$$
3	1	orcd	$$⊢\phi \to \left(\psi \vee \theta \right)$$
4	2	olcd	$$⊢\chi \to \left(\psi \vee \theta \right)$$
5	3 4	jaoi	$$⊢\left(\phi \vee \chi \right)\to \left(\psi \vee \theta \right)$$