let UN be Universe; :: thesis: ( 0 is Element of UN & 1 is Element of UN & 2 is Element of UN )
thus 0 is Element of UN by CLASSES2:56; :: thesis: ( 1 is Element of UN & 2 is Element of UN )
( {} is Element of UN & 1 = succ 0 ) by CLASSES2:56;
hence A1: 1 is Element of UN by Th20; :: thesis: 2 is Element of UN
2 = succ 1 ;
hence 2 is Element of UN by A1, Th20; :: thesis: verum