Theorem orri 873

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 859	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 233	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 858

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 209  df-or 859

This theorem is referenced by:  orci  876  olci  877  pm2.25  900  curryax  904  exmid  905  pm2.13  908  pm5.11g  956  pm5.12  958  pm5.14  959  pm5.55  961  pm3.12  1006  pm5.15  1025  pm5.54  1030  4exmid  1062  rb-ax2  1772  rb-ax3  1773  rb-ax4  1774  exmo  2568  axi12  2731  exmidne  2966  ifeqor  4531  fvbr0  6890  letrii  11305  clwwlknondisj  30259  poimirlem26  38109  tsbi3  38598  tsan2  38605  tsan3  38606  clsk1indlem2  44582