Theorem ori 862

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 849	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbi 230	1 ⊢ (¬ 𝜑 → 𝜓)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 848

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 207  df-or 849

This theorem is referenced by:  3ori  1427  mtpor  1772  fvrn0  6863  eliman0  6872  onuninsuci  7785  omelon2  7824  infensuc  9087  rankxpsuc  9800  cardlim  9890  alephreg  10499  tskcard  10698  sinhalfpilem  26443  ltsres  27643