Which clause in section 1 of the fourteenth amendment was undermined by the slaughterhouse cases?

The correct answer is the  privileges or immunities clause

Basically, the supreme court made a decision that people have something like two citizenships, one the federal one of the United States of America and one of the state that they are from. According to them, the fourteenth amendment protects these privileges and immunities to those with US citizenship, but not to those that have those state citizenship.