Theorem orri 861

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 847	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 230	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 846

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 206  df-or 847

This theorem is referenced by:  orci  864  olci  865  pm2.25  888  curryax  892  exmid  893  pm2.13  896  pm5.11g  942  pm5.12  944  pm5.14  945  pm5.55  947  pm3.12  992  pm5.15  1011  pm5.54  1016  4exmid  1050  rb-ax2  1748  rb-ax3  1749  rb-ax4  1750  exmo  2532  axi12  2697  exmidne  2947  ifeqor  4580  fvbr0  6926  letrii  11370  clwwlknondisj  29934  poimirlem26  37119  tsbi3  37608  tsan2  37615  tsan3  37616  clsk1indlem2  43472