Relu does have 0 gradient by definition, then why gradient vanish is not a problem for x < 0?

By definition, Relu is max(0,f(x)). Then its gradient is defined as: 1 if x > 0 and 0 if x < 0.

Wouldn't this mean the gradient is always 0 (vanishes) when x < 0? Then why do we say Relu doesn't suffer from the gradient vanish problem?