theorem Th55:
  [x1,x2,x3] in [: X1,X2,X3 :] iff x1 in X1 & x2 in X2 & x3 in X3
proof
A1: [x1,x2] in [:X1,X2:] iff x1 in X1 & x2 in X2 by ZFMISC_1:87;
  [:X1,X2,X3:] = [:[:X1,X2:],X3:] by ZFMISC_1:def 3;
  hence thesis by A1,ZFMISC_1:87;
end;
