A theory is either true or false. Galileo's observations of Jupiter's satellites showed that the Ptolemaic theory of the motion of celestial bodies is false. Therefore, since the Copernican theory of planetary motion is inconsistent with the Ptolemaic account, Galileo's observations of Jupiter's satellites proved the truth of the Copernican theory.
The argument above is open to the objection that it makes the questionable assumption that
whoever first observed something inconsistent with the truth of the Ptolemaic theory should be credited with having proved that theory false
there are some possible observations that would be inconsistent with the account given by the Copernican theory but consistent with the account given by the Ptolemaic theory
the Ptolemaic and Copernican theories, being inconsistent, cannot both be based on exactly the same evidence
numerous counterexamples were necessary in order to show the Ptolemaic theory to be false
the Ptolemaic and Copernican theories, being inconsistent, cannot both be false