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;
reserve e,u for object,
  A for Subset of X;

theorem Th96:
  rng(f|{X}) c= {f.X}
proof
  let x be object;
  assume x in rng(f|{X});
  then consider y being object such that
A1: y in dom(f|{X}) and
A2: x = (f|{X}).y by Def3;
  dom(f|{X}) c= {X} by RELAT_1:58;
  then y = X by A1,TARSKI:def 1;
  then x = f.X by A1,A2,Th46;
  hence thesis by TARSKI:def 1;
end;
