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
  H/(x,x) = H
proof
A1: now
    let a be object;
    assume
A2: a in dom H;
    then H.a = x implies H/(x,x).a = x by Def3;
    hence H.a = H/(x,x).a by A2,Def3;
  end;
  dom (H/(x,x)) = dom H by Def3;
  hence thesis by A1,FUNCT_1:2;
end;
