reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem Th24:
  <:pr1(a,b),pr2(a,b):> = id(a[x]b)
proof
A1: Hom(a[x]b,b) <> {} by Th19;
  then
A2: pr2(a,b)*(id(a[x]b)) = pr2(a,b) by CAT_1:29;
A3: Hom(a[x]b,a) <> {} by Th19;
  then pr1(a,b)*(id(a[x]b)) = pr1(a,b) by CAT_1:29;
  hence thesis by A3,A1,A2,Def10;
end;
