Theorem olci 744

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 723	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑)

This proof depends on syntax axioms:   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  falortru  1456  sucidg  4561  finexdc  7207  elssdc  7209  fissfi  7263  finomni  7480  indpi  7709  1ap0  8919  iap0  9530  pnf0xnn0  9639  bcn1  11198  sum0  12157  prod0  12354  odd2np1lem  12641  lcm0val  12845  ballotfilemcdc  13225  usgrexmpldifpr  16502  konigsberglem1  16741  ex-or  16748  dcapnconst  17123