Theorem olci 380

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

Hypothesis

Ref	Expression
orci.1	⊢ φ

Assertion

Ref	Expression
olci	⊢ (ψ ∨ φ)

Proof of Theorem olci

Step	Hyp	Ref	Expression
1		orci.1	. . 3 ⊢ φ
2	1	a1i 10	. 2 ⊢ (¬ ψ → φ)
3	2	orri 365	1 ⊢ (ψ ∨ φ)

Syntax hints:  ¬ wn 3   ∨ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  falortru  1342  ltcirr  6273