Helo,I need confirmation on this concept:

Let (M,d) be a metric space and $\displaystyle \phi:M\rightarrow N$ be a bijective map ,then we can make N a metric space isometric to M by defining a metric $\displaystyle d_1$ by : distance between

$\displaystyle \phi(x)$ and $\displaystyle \phi(y)$ equals distance between x and y

$\displaystyle d_1(\phi(x),\phi(y))=d(x,y)$