Theorem orri 862

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 848	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 231	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  orci  865  olci  866  pm2.25  889  curryax  893  exmid  894  pm2.13  897  pm5.11g  945  pm5.12  947  pm5.14  948  pm5.55  950  pm3.12  995  pm5.15  1014  pm5.54  1019  4exmid  1051  rb-ax2  1753  rb-ax3  1754  rb-ax4  1755  exmo  2541  axi12  2705  exmidne  2942  ifeqor  4552  fvbr0  6905  letrii  11360  clwwlknondisj  30092  poimirlem26  37670  tsbi3  38159  tsan2  38166  tsan3  38167  clsk1indlem2  44066