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Metamath Proof Explorer

Theorem negpitopissre

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

		Ref	Expression
	Assertion	negpitopissre	$⊢ (- π, π] \subseteq ℝ$

Step	Hyp	Ref	Expression
1		pire	$⊢ π \in ℝ$
2	1	renegcli	$⊢ - π \in ℝ$
3	2	rexri	$⊢ - π \in ℝ^{*}$
4		iocssre	$⊢ (- π \in ℝ^{*} \land π \in ℝ) \to (- π, π] \subseteq ℝ$
5	3 1 4	mp2an	$⊢ (- π, π] \subseteq ℝ$