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 Th22:
  X1<>{} & X2<>{} & X3<>{} implies ( [:X1,X2,X3:] = [:Y1,Y2,Y3:]
  implies X1=Y1 & X2=Y2 & X3=Y3)
proof
A1: [:X1,X2,X3:] = [:[:X1,X2:],X3:] by ZFMISC_1:def 3;
  assume
A2: X1<>{} & X2<>{};
  assume
A3: X3<>{};
  assume [:X1,X2,X3:] = [:Y1,Y2,Y3:];
  then
A4: [:[:X1,X2:],X3:] = [:[:Y1,Y2:],Y3:] by A1,ZFMISC_1:def 3;
  then [:X1,X2:] = [:Y1,Y2:] by A2,A3,ZFMISC_1:110;
  hence thesis by A2,A3,A4,ZFMISC_1:110;
end;
