reserve v,x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2 for object,
  X,X1,X2,X3,X4,Y,Y1,Y2,Y3,Y4,Y5,
  Z,Z1,Z2,Z3,Z4,Z5 for set;
reserve p for pair object;

theorem Th4:
  z in [:X,Y:] implies z`1 in X & z`2 in Y
proof
  assume z in [:X,Y:];
  then consider x,y being object such that
A1: x in X & y in Y & z=[x,y] by ZFMISC_1:def 2;
  thus thesis by A1;
