Theorem pire

Description: _pi is a real number. (Contributed by Paul Chapman, 23-Jan-2008)

	Ref	Expression
Assertion	pire	$$⊢\mathrm{\pi }\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		pilem3	$$⊢\left(\mathrm{\pi }\in \left(2,4\right)\wedge \sin \mathrm{\pi }=0\right)$$
2	1	simpli	$$⊢\mathrm{\pi }\in \left(2,4\right)$$
3		elioore	$$⊢\mathrm{\pi }\in \left(2,4\right)\to \mathrm{\pi }\in ℝ$$
4	2 3	ax-mp	$$⊢\mathrm{\pi }\in ℝ$$