Theorem orri 391

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 385	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 221	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 383

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 385

This theorem is referenced by:  orci  405  olci  406  pm2.25  419  exmid  431  pm2.13  434  pm3.12  521  pm5.11  928  pm5.12  929  pm5.14  930  pm5.15  933  pm5.55  939  pm5.54  943  4exmid  997  rb-ax2  1678  rb-ax3  1679  rb-ax4  1680  exmo  2495  axi12  2600  axbnd  2601  exmidne  2804  ifeqor  4132  fvbr0  6215  letrii  10162  clwwlksndisj  26973  bj-curry  32542  poimirlem26  33435  tsim2  33938  tsbi3  33942  tsan2  33949  tsan3  33950  clsk1indlem2  38340