If $A \le_p B$ and $B\in NP$, does it necessarily follow that $A\in NP$?

A quick yes/no comment is enough, a proof would be nice :-)

If $A \le_p B$ and $B\in NP$, does it necessarily follow that $A\in NP$?
($\le_p$ is a polynomial many-one reduction)

A quick yes/no comment is enough, a proof would be nice :-)