text: I was taught in Catholic high school that there were only two infallible teachings:   Immaculate Conception and Assumption.    
  
  Later, I pondered this and thought:  wait a second, that can't be right.  Vatican I itself has to be infallible.   Otherwise, if it wasn't, it could have been wrong about infallibility itself.  
  
  There are numerous ex cathedra teachings in Church history, not just two.  
  
  The reason any ecumenical council is infallible on a given teaching on faith and morals, is only because the pope promulgates it ex cathedra.  
  
  The Council of Florence taught about the salvation dogma, and that teaching is ex cathedra because of Pope Eugene IV. 
  
  Also, Vatican I taught that not only ex cathedra/extraordinary Magisterium teachings are infallible.... Vatican I also taught that the universal ordinary Magisterium is infallible as well.