Theorem negpilt0

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

	Ref	Expression
Assertion	negpilt0	$$⊢-\mathrm{\pi }<0$$

Proof

Step	Hyp	Ref	Expression
1		pipos	$$⊢0<\mathrm{\pi }$$
2		pire	$$⊢\mathrm{\pi }\in ℝ$$
3		lt0neg2	$$⊢\mathrm{\pi }\in ℝ\to \left(0<\mathrm{\pi }\leftrightarrow -\mathrm{\pi }<0\right)$$
4	2 3	ax-mp	$$⊢0<\mathrm{\pi }\leftrightarrow -\mathrm{\pi }<0$$
5	1 4	mpbi	$$⊢-\mathrm{\pi }<0$$