Explain why it is harder to remove an inner shell electrons than a valence electron from an atom

It makes sense that an inner shell electron would be tougher to remove than a valence electron because the inner shell electron is closer to the positive nucleus of the atom. Seeing as an electron caries a negative charge it would be too attracted to the positive core to leave readily. Also, the inner shell electrons are constantly repelling electrons outside of it's energy level (however the reason these electrons outside innershell energy levels don't simply fly away is the charge of the positive core overcomes the smaller charges of the comparably negligible inner shell electrons, but that repulsion is still there so keep that in mind)