Theorem ori 860

Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.)

Hypothesis

Ref	Expression
ori.1	⊢ (𝜑 ∨ 𝜓)

Assertion

Ref	Expression
ori	⊢ (¬ 𝜑 → 𝜓)

Proof of Theorem ori

Step	Hyp	Ref	Expression
1		ori.1	. 2 ⊢ (𝜑 ∨ 𝜓)
2		df-or 847	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbi 233	1 ⊢ (¬ 𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 846

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 847

This theorem is referenced by:  3ori  1425  mtpor  1777  fvrn0  6715  eliman0  6722  onuninsuci  7587  omelon2  7624  infensuc  8758  rankxpsuc  9397  cardlim  9487  alephreg  10095  tskcard  10294  sinhalfpilem  25221  sltres  33521