reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  (Y c= X & Z c= X & for V st Y c= V & Z c= V holds X c= V) implies X = Y \/ Z
proof
  assume that
A1: Y c= X & Z c= X and
A2: Y c= V & Z c= V implies X c= V;
  Y c= Y \/ Z & Z c= Y \/ Z by Th7;
  hence X c= Y \/ Z by A2;
  thus thesis by A1,Th8;
end;
