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;

theorem Th21:
  X1 <> {} & X2 <> {} & X3 <> {} iff [:X1,X2,X3:] <> {}
proof
A1: X1 <> {} & X2 <> {} iff [:X1,X2:] <> {} by ZFMISC_1:90;
  [:[:X1,X2:],X3:] = [:X1,X2,X3:] by ZFMISC_1:def 3;
  hence thesis by A1,ZFMISC_1:90;
end;
