Theorem olci 687

Description: Deduction introducing a disjunct. (Contributed by NM, 19-Jan-2008.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypothesis

Ref	Expression
orci.1	⊢ 𝜑

Assertion

Ref	Expression
olci	⊢ (𝜓 ∨ 𝜑)

Proof of Theorem olci

Step	Hyp	Ref	Expression
1		orci.1	. 2 ⊢ 𝜑
2		olc 668	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 7	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 665

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-io 666

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  falortru  1344  sucidg  4252  finexdc  6672  finomni  6850  indpi  6955  1ap0  8121  iap0  8693  pnf0xnn0  8797  bcn1  10220  sum0  10834  odd2np1lem  11204  lcm0val  11379  ex-or  11915