Theorem orci 703

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 684	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
3	1, 2	ax-mp 7	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:   ∨ wo 680

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-io 681

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  truorfal  1367  prid1g  3593  onsucelsucexmidlem1  4403  regexmidlemm  4407  nn0suc  4478  nndceq0  4491  0elnn  4492  acexmidlem2  5725  exmidaclem  7012  indpi  7098  sup3exmid  8625  nn1gt1  8664  nneoor  9057  mnfltpnf  9464  bcpasc  10405