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	|- ph

Assertion

Ref	Expression
olci	|- ( ps \/ ph )

Proof of Theorem olci

Step	Hyp	Ref	Expression
1		orci.1	. 2 |- ph
2		olc 723	. 2 |- ( ph -> ( ps \/ ph ) )
3	1, 2	ax-mp 5	1 |- ( ps \/ ph )

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  4563  finexdc  7211  elssdc  7213  fissfi  7267  finomni  7486  indpi  7715  1ap0  8926  iap0  9539  pnf0xnn0  9648  bcn1  11218  sum0  12180  prod0  12377  odd2np1lem  12664  lcm0val  12868  ballotfilemcdc  13281  bpos1  16310  usgrexmpldifpr  16695  konigsberglem1  16934  ex-or  16941  dcapnconst  17318