Theorem lt0ne0

Description: A number which is less than zero is not zero. (Contributed by Stefan O'Rear, 13-Sep-2014)

	Ref	Expression
Assertion	lt0ne0	$$⊢\left(A\in ℝ\wedge A<0\right)\to A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		ltne	$$⊢\left(A\in ℝ\wedge A<0\right)\to 0\ne A$$
2	1	necomd	$$⊢\left(A\in ℝ\wedge A<0\right)\to A\ne 0$$