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	$$⊢P\mathrm{OutsideOf}⟨Q,R⟩\to P\mathrm{Colinear}⟨Q,R⟩$$

Proof

Step	Hyp	Ref	Expression
1		broutsideof	$$⊢P\mathrm{OutsideOf}⟨Q,R⟩\leftrightarrow \left(P\mathrm{Colinear}⟨Q,R⟩\wedge \neg P\mathrm{Btwn}⟨Q,R⟩\right)$$
2	1	simplbi	$$⊢P\mathrm{OutsideOf}⟨Q,R⟩\to P\mathrm{Colinear}⟨Q,R⟩$$