Theorem neg1lt0

Description: -1 is less than 0. (Contributed by David A. Wheeler, 8-Dec-2018)

	Ref	Expression
Assertion	neg1lt0	$$⊢-1<0$$

Proof

Step	Hyp	Ref	Expression
1		0lt1	$$⊢0<1$$
2		1re	$$⊢1\in ℝ$$
3		lt0neg2	$$⊢1\in ℝ\to \left(0<1\leftrightarrow -1<0\right)$$
4	2 3	ax-mp	$$⊢0<1\leftrightarrow -1<0$$
5	1 4	mpbi	$$⊢-1<0$$