reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem Th47:
  x in dom f /\ X implies (f|X).x = f.x
proof
  assume x in dom f /\ X;
  then x in dom(f|X) by RELAT_1:61;
  hence thesis by Th46;
end;
