Theorem orri 876

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 862	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 234	1 ⊢ (𝜑 ∨ 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  orci  879  olci  880  pm2.25  903  curryax  907  exmid  908  pm2.13  911  pm5.11g  958  pm5.12  960  pm5.14  961  pm5.55  963  pm3.12  1009  pm5.15  1030  pm5.54  1035  4exmid  1067  rb-ax2  1786  rb-ax3  1787  rb-ax4  1788  exmo  2573  axi12  2736  exmidne  2971  ifeqor  4544  fvbr0  6915  letrii  11353  clwwlknondisj  30499  poimirlem26  38338  tsbi3  38825  tsan2  38832  tsan3  38833  clsk1indlem2  44809