Theorem orci 682

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
orci	⊢ (𝜑 ∨ 𝜓)

Proof of Theorem orci

Step	Hyp	Ref	Expression
1		orci.1	. 2 ⊢ 𝜑
2		orc 665	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
3	1, 2	ax-mp 7	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:   ∨ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  truorfal  1337  prid1g  3496  onsucelsucexmidlem1  4271  regexmidlemm  4275  nn0suc  4345  nndceq0  4357  0elnn  4358  acexmidlem2  5529  indpi  6532  nn1gt1  8072  nneoor  8449  mnfltpnf  8860  bcpasc  9693