reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;
reserve X,X1,X2,X3,X4,Y for set;

theorem Th12:
 x in proj1_3 X implies ex y,z st [x,y,z] in X
proof assume x in proj1_3 X;
  then consider y such that
A1: [x,y] in proj1 X by Def12;
  consider z such that
A2: [[x,y],z] in X by A1,Def12;
 take y,z;
 thus thesis by A2;
end;
