Let $M$ and $N$ be smooth manifolds, and $A\subset M$, $B\subset N$ be smooth embedded submanifolds. I am looking for a reference for a theorem on the following lines:

The set of smooth maps $h\in C^\infty(M,N)$ such that $h\bigr|_{A}\pitchfork B$ is generic, i.e. it contains a countable intersection of open and dense subsets, in both the strong and weak topologies.

With the transversality assumption I really mean that the map $h\bigr|_{A}:A\rightarrow N$ is transverse to $B$. Thus I want that for each $a\in A$, such that $h(a)\in B$ that $dh T_aA+T_{h(a)}B=T_{h(a)}N$.

I expect that this is true. I have a sketch of a proof of a slightly more simple situation, which is where I need to apply the theorem, but the details are a bit messy. My question is therefore: Where can I find this (or a similar) theorem in the literature?

Differential Topology, chapter II on transversality, Theorem 2.1(b) $\endgroup$