Theorem orri 858

Description: Infer disjunction from implication. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
orri.1	⊢ (¬ 𝜑 → 𝜓)

Assertion

Ref	Expression
orri	⊢ (𝜑 ∨ 𝜓)

Proof of Theorem orri

Step	Hyp	Ref	Expression
1		orri.1	. 2 ⊢ (¬ 𝜑 → 𝜓)
2		df-or 844	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 233	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-or 844

This theorem is referenced by:  orci  861  olci  862  pm2.25  886  curryax  890  exmid  891  pm2.13  894  pm5.11g  940  pm5.12  942  pm5.14  943  pm5.55  945  pm3.12  990  pm5.15  1009  pm5.54  1014  4exmid  1046  rb-ax2  1754  rb-ax3  1755  rb-ax4  1756  exmo  2624  axi12  2791  axi12OLD  2792  axbndOLD  2794  exmidne  3028  ifeqor  4518  fvbr0  6699  letrii  10767  clwwlknondisj  27892  poimirlem26  34920  tsbi3  35415  tsan2  35422  tsan3  35423  clsk1indlem2  40399