reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

theorem Th184:
  x <> y implies not x in variables_in (H/(x,y))
proof
  assume
A1: x <> y;
  assume x in variables_in (H/(x,y));
  then consider a being object such that
A2: a in dom (H/(x,y)) and
A3: x = H/(x,y).a by FUNCT_1:def 3;
A4: dom (H/(x,y)) = dom H by Def3;
  then H.a = x implies H/(x,y).a = y by A2,Def3;
  hence contradiction by A1,A2,A3,A4,Def3;
end;
