Theorem olci 721

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 700	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑)

Syntax hints:   ∨ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  falortru  1385  sucidg  4338  finexdc  6796  finomni  7012  indpi  7157  1ap0  8359  iap0  8950  pnf0xnn0  9054  bcn1  10511  sum0  11164  odd2np1lem  11576  lcm0val  11753  ex-or  12944