Theorem ori 894

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 881	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbi 222	1 ⊢ (¬ 𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 880

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 199  df-or 881

This theorem is referenced by:  3ori  1554  mtpor  1871  exmoeuOLD  2686  fvrn0  6462  eliman0  6470  onuninsuci  7302  omelon2  7339  infensuc  8408  rankxpsuc  9023  cardlim  9112  alephreg  9720  tskcard  9919  sinhalfpilem  24616  sltres  32355