If the original Vista installation is OEM, it is "legally" tied to the computer. Meaning it is not transferable to another computer. However, a Windows 7 upgrade can be installed without the original operating system installed. There is a technique described in the tutorials section.
If you do this and then do not use the old Windows Vista operating system, you should be OK. The Windows 7 upgrade has its own license number, so it does not re-use the one from Vista. I can't recall, but you may have to enter in the Vista license number during the installation. If so, then definitely do not use the Vista installation discs for another computer. Legally, it is supposed to be the same computer, but Microsoft does not enforce it. As long as you purchased the Windows 7 installation, Microsoft gets their money and it shouldn't be their concern as to which computer it is on. The only caveat is not using the older Vista operating system, since it has technically been upgraded. If the Vista license number was required during Windows 7 installation, then your Vista copy may be logged with Microsoft as a deactivated operating system and would fail authentication.