Theorem orri 390

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 384	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 220	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

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 196  df-or 384

This theorem is referenced by:  orci  404  olci  405  pm2.25  418  exmid  430  pm2.13  433  pm3.12  520  pm5.11  924  pm5.12  925  pm5.14  926  pm5.15  929  pm5.55  937  pm5.54  941  rb-ax2  1669  rb-ax3  1670  rb-ax4  1671  exmo  2483  axi12  2588  axbnd  2589  exmidne  2792  ifeqor  4082  fvbr0  6125  letrii  10041  numclwwlkdisj  26607  bj-curry  31712  poimirlem26  32605  tsim2  33108  tsbi3  33112  tsan2  33119  tsan3  33120  clsk1indlem2  37360  clwwlksndisj  41280