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;
reserve R for Relation;
reserve xx1 for Element of X1,
  xx2 for Element of X2,
  xx3 for Element of X3;

theorem Th39:
  X1 <> {} & X2 <> {} & X3 <> {} & X4 <> {} iff [:X1,X2,X3,X4:] <>
  {}
proof
A1: [:[:X1,X2,X3:],X4:] = [:X1,X2,X3,X4:] by ZFMISC_1:def 4;
  X1 <> {} & X2 <> {} & X3 <> {} iff [:X1,X2,X3:] <> {} by Th21;
  hence thesis by A1,ZFMISC_1:90;
end;
