The Supremacy clause is defined in detail in Marbury V Madison, 5 U.S. 137 (1803). A superb opinion by John Marshall against of all people, James Madison as Secretary of State.

"So if a law be in opposition to the constitution; if both the law and the constitution apply to a particular case, so that the court must either decide that case conformably to the law, disregarding the constitution; or conformably to the constitution, disregarding the law; the court must determine which of these conflicting rules governs the case. This is of the very essence of judicial duty.

If, then, the courts are to regard the constitution, and the constitution is superior to any ordinary act of the legislature, the constitution, and not such ordinary act, must govern the case to which they both apply.

Those, then, who controvert the principle that the constitution is to be considered, in court, as a paramount law, are reduced to the necessity of maintaining that courts must close their eyes on the constitution, and see only the law.

This doctrine would subvert the very foundation of all written constitutions. It would declare that an act which, according to the principles and theory of our government, is entirely void, is yet, in practice, completely obligatory. It would declare that if the legislature shall do what is expressly forbidden, such act, notwithstanding the express prohibition, is in reality effectual. It would be giving to the legislature a practical and real omnipotence, with the same breath which professes to restrict their powers within narrow limits. It is prescribing limits, and declaring that those limits may be passed at pleasure."