Theorem negpitopissre

Description: The interval ( -upi (,] pi ) is a subset of the reals. (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Assertion	negpitopissre	⊢ ( - π (,] π ) ⊆ ℝ

Proof

Step	Hyp	Ref	Expression
1		pire	⊢ π ∈ ℝ
2	1	renegcli	⊢ - π ∈ ℝ
3	2	rexri	⊢ - π ∈ ℝ*
4		iocssre	⊢ ( ( - π ∈ ℝ* ∧ π ∈ ℝ ) → ( - π (,] π ) ⊆ ℝ )
5	3 1 4	mp2an	⊢ ( - π (,] π ) ⊆ ℝ