Theorem orri 389

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 383	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 219	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 381

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 195  df-or 383

This theorem is referenced by:  orci  403  olci  404  pm2.25  417  exmid  429  pm2.13  432  pm3.12  519  pm5.11  923  pm5.12  924  pm5.14  925  pm5.15  928  pm5.55  936  pm5.54  940  rb-ax2  1668  rb-ax3  1669  rb-ax4  1670  exmo  2482  axi12  2587  axbnd  2588  exmidne  2791  ifeqor  4081  fvbr0  6110  letrii  10013  numclwwlkdisj  26373  bj-curry  31518  poimirlem26  32401  tsim2  32904  tsbi3  32908  tsan2  32915  tsan3  32916  clsk1indlem2  37156  clwwlksndisj  41275