Theorem olci 734

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 713	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-io 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  falortru  1427  sucidg  4467  finexdc  7006  finomni  7249  indpi  7462  1ap0  8670  iap0  9267  pnf0xnn0  9372  bcn1  10910  sum0  11743  prod0  11940  odd2np1lem  12227  lcm0val  12431  ex-or  15732  dcapnconst  16074