This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem negpilt0

Description: Negative _pi is negative. (Contributed by Glauco Siliprandi, 11-Dec-2019)

		Ref	Expression
	Assertion	negpilt0	$⊢ - π < 0$

Step	Hyp	Ref	Expression
1		pipos	$⊢ 0 < π$
2		pire	$⊢ π \in ℝ$
3		lt0neg2	$⊢ π \in ℝ \to (0 < π \leftrightarrow - π < 0)$
4	2 3	ax-mp	$⊢ 0 < π \leftrightarrow - π < 0$
5	1 4	mpbi	$⊢ - π < 0$