Theorem orri 390

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 384	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 221	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

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 197  df-or 384

This theorem is referenced by:  orci  404  olci  405  pm2.25  418  exmid  430  pm2.13  433  pm3.12  520  pm5.11  946  pm5.12  947  pm5.14  948  pm5.15  951  pm5.55  957  pm5.54  963  4exmid  1021  rb-ax2  1718  rb-ax3  1719  rb-ax4  1720  exmo  2523  axi12  2629  axbnd  2630  exmidne  2833  ifeqor  4165  fvbr0  6253  letrii  10200  clwwlknondisj  27086  clwwlknondisjOLD  27090  bj-curry  32667  poimirlem26  33565  tsim2  34068  tsbi3  34072  tsan2  34079  tsan3  34080  clsk1indlem2  38657