Theorem ori 875

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 862	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
3	1, 2	mpbi 233	1 ⊢ (¬ 𝜑 → 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  3ori  1451  mtpor  1802  fvrn0  6918  eliman0  6927  onuninsuci  7855  omelon2  7894  infensuc  9182  rankxpsuc  9906  cardlim  10060  alephreg  10674  tskcard  10873  sinhalfpilem  26801  ltsres  28028  goldratval  48072