Theorem olci 684

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 665	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 7	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 662

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-io 663

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  falortru  1341  sucidg  4210  finexdc  6548  finomni  6717  indpi  6822  1ap0  7985  iap0  8549  pnf0xnn0  8653  bcn1  10015  odd2np1lem  10666  lcm0val  10841  ex-or  11007