Theorem orri 871

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 857	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbir 233	1 ⊢ (𝜑 ∨ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 856

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 209  df-or 857

This theorem is referenced by:  orci  874  olci  875  pm2.25  898  curryax  902  exmid  903  pm2.13  906  pm5.11g  954  pm5.12  956  pm5.14  957  pm5.55  959  pm3.12  1004  pm5.15  1023  pm5.54  1028  4exmid  1060  rb-ax2  1763  rb-ax3  1764  rb-ax4  1765  exmo  2559  axi12  2722  exmidne  2957  ifeqor  4522  fvbr0  6879  letrii  11294  clwwlknondisj  30248  poimirlem26  38083  tsbi3  38572  tsan2  38579  tsan3  38580  clsk1indlem2  44556