Theorem ori 200

Description: Inference from disjunction definition.

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 197	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
3	1, 2	mpbi 164	1 ⊢ (¬ φ → ψ)

Syntax hints:  ¬ wn 1   → wi 2   ∨ wo 195

This theorem is referenced by:  moexex 1058  mo2icl 1434  mosubop 1911  onuninsuc 2356  omelon 3476  cardom 3632  cardlim 3657  nneo 4719  absgt0 4842

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197

metamath.org