Theorem orri 859

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 845	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 230	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844

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 206  df-or 845

This theorem is referenced by:  orci  862  olci  863  pm2.25  887  curryax  891  exmid  892  pm2.13  895  pm5.11g  941  pm5.12  943  pm5.14  944  pm5.55  946  pm3.12  991  pm5.15  1010  pm5.54  1015  4exmid  1049  rb-ax2  1756  rb-ax3  1757  rb-ax4  1758  exmo  2542  axi12  2707  exmidne  2953  ifeqor  4510  fvbr0  6801  letrii  11100  clwwlknondisj  28475  poimirlem26  35803  tsbi3  36293  tsan2  36300  tsan3  36301  clsk1indlem2  41652