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 ∈ ℝ
3		lt0neg2	⊢ ( 1 ∈ ℝ → ( 0 < 1 ↔ - 1 < 0 ) )
4	2 3	ax-mp	⊢ ( 0 < 1 ↔ - 1 < 0 )
5	1 4	mpbi	⊢ - 1 < 0