reserve x,y,z,x1,x2,x3,x4,y1,y2,s for Variable,
  M for non empty set,
  a,b for set,
  i,j,k for Element of NAT,
  m,m1,m2,m3,m4 for Element of M,
  H,H1,H2 for ZF-formula,
  v,v9,v1,v2 for Function of VAR,M;

theorem Th4:
  not x in variables_in H implies (M,v |= H iff M,v |= All(x,H))
proof
  Free H c= variables_in H by ZF_LANG1:151;
  then
A1: x in Free H implies x in variables_in H;
  v/(x,v.x) = v by FUNCT_7:35;
  hence thesis by A1,ZFMODEL1:10,ZF_LANG1:71;
end;
