Theorem reneg1lt0

Description: Lemma for sn-inelr . (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 e. RR
3		relt0neg2	|- ( 1 e. RR -> ( 0 < 1 <-> ( 0 -R 1 ) < 0 ) )
4	2 3	ax-mp	|- ( 0 < 1 <-> ( 0 -R 1 ) < 0 )
5	1 4	mpbi	|- ( 0 -R 1 ) < 0