Theorem subge0i

Description: Nonnegative subtraction. (Contributed by NM, 13-Aug-2000)

	Ref	Expression
Hypotheses	lt2.1	$$⊢A\in ℝ$$
	lt2.2	$$⊢B\in ℝ$$
Assertion	subge0i	$$⊢0\le A-B\leftrightarrow B\le A$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		lt2.2	$$⊢B\in ℝ$$
3		subge0	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(0\le A-B\leftrightarrow B\le A\right)$$
4	1 2 3	mp2an	$$⊢0\le A-B\leftrightarrow B\le A$$