Theorem orri 868

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 854	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 232	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 853

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 208  df-or 854

This theorem is referenced by:  orci  871  olci  872  pm2.25  895  curryax  899  exmid  900  pm2.13  903  pm5.11g  951  pm5.12  953  pm5.14  954  pm5.55  956  pm3.12  1001  pm5.15  1020  pm5.54  1025  4exmid  1057  rb-ax2  1760  rb-ax3  1761  rb-ax4  1762  exmo  2546  axi12  2710  exmidne  2945  ifeqor  4513  fvbr0  6861  letrii  11269  clwwlknondisj  30206  poimirlem26  38020  tsbi3  38509  tsan2  38516  tsan3  38517  clsk1indlem2  44493