Theorem orim2d

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995)

	Ref	Expression
Hypothesis	orim1d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	orim2d	$$⊢\phi \to \left(\left(\theta \vee \psi \right)\to \left(\theta \vee \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		orim1d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		idd	$$⊢\phi \to \left(\theta \to \theta \right)$$
3	2 1	orim12d	$$⊢\phi \to \left(\left(\theta \vee \psi \right)\to \left(\theta \vee \chi \right)\right)$$