Theorem outsideofcol

Description: Outside of implies colinearity. (Contributed by Scott Fenton, 26-Oct-2013) (Revised by Mario Carneiro, 19-Apr-2014)

	Ref	Expression
Assertion	outsideofcol	⊢ ( 𝑃 OutsideOf ⟨ 𝑄 , 𝑅 ⟩ → 𝑃 Colinear ⟨ 𝑄 , 𝑅 ⟩ )

Proof

Step	Hyp	Ref	Expression
1		broutsideof	⊢ ( 𝑃 OutsideOf ⟨ 𝑄 , 𝑅 ⟩ ↔ ( 𝑃 Colinear ⟨ 𝑄 , 𝑅 ⟩ ∧ ¬ 𝑃 Btwn ⟨ 𝑄 , 𝑅 ⟩ ) )
2	1	simplbi	⊢ ( 𝑃 OutsideOf ⟨ 𝑄 , 𝑅 ⟩ → 𝑃 Colinear ⟨ 𝑄 , 𝑅 ⟩ )