Where can one find the proof of the following fact:

If there are two orientation-preserving diffeomorphisms $\phi_0$ and $\phi_1$ of $R^n$, then there exists a homotopy $\phi(t)$, such that $\phi(0)$ = $\phi_0$, $\phi(1)$ = $\phi_1$, and $\phi(t)$ is a diffeomorphism for any $t$ (and $\phi$ is smooth for all variables).

This is easy to prove for $n=1$, and relatively easy for $n=2$, but for an arbitrary $n$ seems difficult.

This fact is used in the knot theory to justify the coincidence of two definitions of the knot equivalence.