reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem
  for X being set, f,g being Function st X c= dom f & f c= g holds f|X = g|X
proof
  let X be set, f,g be Function such that
A1: X c= dom f;
  assume f c= g;
  hence f|X = g|(dom f)|X by Th21
    .= g|((dom f) /\ X) by RELAT_1:71
    .= g|X by A1,XBOOLE_1:28;
end;
