Theorem orri 875

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 861	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 234	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 860

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 210  df-or 861

This theorem is referenced by:  orci  878  olci  879  pm2.25  902  curryax  906  exmid  907  pm2.13  910  pm5.11g  958  pm5.12  960  pm5.14  961  pm5.55  963  pm3.12  1009  pm5.15  1028  pm5.54  1033  4exmid  1065  rb-ax2  1776  rb-ax3  1777  rb-ax4  1778  exmo  2572  axi12  2735  exmidne  2970  ifeqor  4535  fvbr0  6898  letrii  11323  clwwlknondisj  30371  poimirlem26  38157  tsbi3  38646  tsan2  38653  tsan3  38654  clsk1indlem2  44630