Theorem reneg1lt0

Description: Negative one is a negative number. (Contributed by SN, 1-Jun-2024)

	Ref	Expression
Assertion	reneg1lt0	$$⊢0{-}_{ℝ}1<0$$

Proof

Step	Hyp	Ref	Expression
1		sn-0lt1	$$⊢0<1$$
2		1re	$$⊢1\in ℝ$$
3		relt0neg2	$$⊢1\in ℝ\to \left(0<1\leftrightarrow 0{-}_{ℝ}1<0\right)$$
4	2 3	ax-mp	$$⊢0<1\leftrightarrow 0{-}_{ℝ}1<0$$
5	1 4	mpbi	$$⊢0{-}_{ℝ}1<0$$