Theorem pire

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

	Ref	Expression
Assertion	pire	⊢ π ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		pilem3	⊢ ( π ∈ ( 2 (,) 4 ) ∧ ( sin ‘ π ) = 0 )
2	1	simpli	⊢ π ∈ ( 2 (,) 4 )
3		elioore	⊢ ( π ∈ ( 2 (,) 4 ) → π ∈ ℝ )
4	2 3	ax-mp	⊢ π ∈ ℝ