Just adding my agreement with the others that you shouldn't have a problem.

The Schengen visa (unlike other types of visas that may be issued by Schengen countries) should allow entry and travel throughout the Schengen zone. The application requirements are mainly in place, as I understand it, to spread out the issuing workload among the member states.

You are supposed to apply for the visa at the consulate/embassy of either your first destination OR your main destination.