reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;
reserve X,X1,X2,X3,X4,Y for set;

theorem Th29:
  proj2 X \ proj2 Y c= proj2(X \ Y)
proof
  let y be object;
  assume
A1: y in proj2 X \ proj2 Y;
  then y in proj2 X by XBOOLE_0:def 5;
  then consider x such that
A2: [x,y] in X by Def13;
  not y in proj2 Y by A1,XBOOLE_0:def 5;
  then not [x,y] in Y by Def13;
  then [x,y] in X \ Y by A2,XBOOLE_0:def 5;
  hence thesis by Def13;
end;
