The first line
[tex]\int \left|\phi(x)\right|^2 dx= \int \left|\psi(p)\right|^2 dp[/itex]<br />
is correct (and is the statement of Parseval's identity). The second line<br />
[tex]\int \left|\phi(x+1)\right|^2 dx= \int \left|\psi(p+1)\right|^2 dp[/itex]<br />
does NOT follow from the first.[/tex][/tex]