reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem Th50:
  not x in Z & not y in Z implies {x,y} misses Z
proof
  assume
A1: ( not x in Z)& not y in Z;
  assume {x,y} meets Z;
  then consider z such that
A2: z in {x,y} /\ Z by XBOOLE_0:4;
  z in {x,y} & z in Z by A2,XBOOLE_0:def 4;
  hence contradiction by A1,TARSKI:def 2;
end;
