Theorem ltnegcon1i

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	ltnegcon1i	$$⊢-A<B\leftrightarrow -B<A$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		lt2.2	$$⊢B\in ℝ$$
3		ltnegcon1	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(-A<B\leftrightarrow -B<A\right)$$
4	1 2 3	mp2an	$$⊢-A<B\leftrightarrow -B<A$$