Theorem orci 379

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
orci	⊢ (φ ∨ ψ)

Proof of Theorem orci

Step	Hyp	Ref	Expression
1		orci.1	. . 3 ⊢ φ
2	1	pm2.24i 136	. 2 ⊢ (¬ φ → ψ)
3	2	orri 365	1 ⊢ (φ ∨ ψ)

Syntax hints:   ∨ 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:  truorfal  1341  prid1g  3826  opkth1g  4131  nnc0suc  4413