# Proving constraints are redundant

I am considering the following question:

Suppose that two constraints in a system are cx $\leq$ 1 and dx $\leq$ 1, where c and d are linearly dependent. If cd $\geq$ 0 does this mean that one of c or d is redundant?

Intuitively, I would say the answer is yes, one of the constraints is redundant. Because cd $\geq$ 0, both c and d are pointing in the same direction (i.e. they are both positive or both negative), any constraint imposed by one will either make redundant or be made redundant by the other. I am having trouble fully forming this idea and proving it more formally - any tips?

$$x \le \frac{1}{c} \qquad \text{and} \qquad x \le \frac{1}{d}$$