Theorem orri 863

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 849	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 231	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 848

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 849

This theorem is referenced by:  orci  866  olci  867  pm2.25  890  curryax  894  exmid  895  pm2.13  898  pm5.11g  946  pm5.12  948  pm5.14  949  pm5.55  951  pm3.12  996  pm5.15  1015  pm5.54  1020  4exmid  1052  rb-ax2  1753  rb-ax3  1754  rb-ax4  1755  exmo  2542  axi12  2706  exmidne  2950  ifeqor  4577  fvbr0  6935  letrii  11386  clwwlknondisj  30130  poimirlem26  37653  tsbi3  38142  tsan2  38149  tsan3  38150  clsk1indlem2  44055