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

theorem
  (X c= Y & X c= Z & for V st V c= Y & V c= Z holds V c= X) implies X = Y /\ Z
proof
  assume that
A1: X c= Y & X c= Z and
A2: V c= Y & V c= Z implies V c= X;
  thus X c= Y /\ Z by A1,Th19;
  Y /\ Z c= Y & Y /\ Z c= Z implies Y /\ Z c= X by A2;
  hence thesis by Th17;
end;
