After changing name servers, does the old SSL get invalidated?

Hi. Quick question. My website has a PositiveSSL, and I want to transfer web hosts. I understand I need to copy the files over and do a CSR request with my new web host to enable the SSL. However, if for some reason I wanted to revert my domain back to the old web host, would that SSL still be seen as “valid” by user’s browsers? Or would they see a warning that this SSL is no longer valid? Thanks

The beauty of server certificates for HTTPS is that they work on DNS names.

The positiveSSL did that come with your webhosting package or did you buy that separately?