Theorem olci 737

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 716	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 713

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-io 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  falortru  1449  sucidg  4507  finexdc  7072  finomni  7315  indpi  7537  1ap0  8745  iap0  9342  pnf0xnn0  9447  bcn1  10988  sum0  11907  prod0  12104  odd2np1lem  12391  lcm0val  12595  ex-or  16110  dcapnconst  16459