Theorem ori 857

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 844	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbi 229	1 ⊢ (¬ 𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843

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 844

This theorem is referenced by:  3ori  1422  mtpor  1774  fvrn0  6784  eliman0  6791  onuninsuci  7662  omelon2  7700  infensuc  8891  rankxpsuc  9571  cardlim  9661  alephreg  10269  tskcard  10468  sinhalfpilem  25525  sltres  33792