Theorem olci

Description: Deduction introducing a disjunct. (Contributed by NM, 19-Jan-2008) (Proof shortened by Wolf Lammen, 14-Nov-2012)

	Ref	Expression
Hypothesis	orci.1	$$⊢\phi$$
Assertion	olci	$$⊢\left(\psi \vee \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orci.1	$$⊢\phi$$
2	1	a1i	$$⊢\neg \psi \to \phi$$
3	2	orri	$$⊢\left(\psi \vee \phi \right)$$