reserve a,b,c,d,e,z for object, A,B,C,D,E for set;

theorem Th3:
  z in [:A,B,C:] implies z = [ z`1_3, z`2_3, z`3_3 ]
proof
  assume
A1: z in [:A,B,C:];
  then
A2: C is non empty by MCART_1:31;
  A is non empty & B is non empty by A1,MCART_1:31;
  then
  ex a being Element of A, b being Element of B, c being Element of C st z
  = [a,b,c] by A1,A2,DOMAIN_1:3;
  hence thesis;
end;
