Theorem lenegcon1i

Description: Contraposition of negative in 'less than or equal to'. (Contributed by NM, 6-Apr-2005)

	Ref	Expression
Hypotheses	lt2.1	$$⊢A\in ℝ$$
	lt2.2	$$⊢B\in ℝ$$
Assertion	lenegcon1i	$$⊢-A\le B\leftrightarrow -B\le A$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		lt2.2	$$⊢B\in ℝ$$
3		lenegcon1	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(-A\le B\leftrightarrow -B\le A\right)$$
4	1 2 3	mp2an	$$⊢-A\le B\leftrightarrow -B\le A$$