theorem
  x in variables_in H implies y in variables_in (H/(x,y))
proof
  assume x in variables_in H;
  then consider a being object such that
A1: a in dom H and
A2: x = H.a by FUNCT_1:def 3;
A3: dom (H/(x,y)) = dom H by Def3;
A4: not y in {0,1,2,3,4} by Th136;
  H/(x,y).a = y by A1,A2,Def3;
  then y in rng (H/(x,y)) by A1,A3,FUNCT_1:def 3;
  hence thesis by A4,XBOOLE_0:def 5;
end;
