Theorem olci 733

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 712	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  falortru  1418  sucidg  4452  finexdc  6965  finomni  7208  indpi  7412  1ap0  8620  iap0  9217  pnf0xnn0  9322  bcn1  10853  sum0  11556  prod0  11753  odd2np1lem  12040  lcm0val  12244  ex-or  15394  dcapnconst  15734