Theorem ltnegcon2i

Description: Contraposition of negative in 'less than'. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	lt2.1	$$⊢A\in ℝ$$
	lt2.2	$$⊢B\in ℝ$$
Assertion	ltnegcon2i	$$⊢A<-B\leftrightarrow B<-A$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		lt2.2	$$⊢B\in ℝ$$
3		ltnegcon2	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(A<-B\leftrightarrow B<-A\right)$$
4	1 2 3	mp2an	$$⊢A<-B\leftrightarrow B<-A$$