reserve x,y,z for Variable,
  H for ZF-formula,
  E for non empty set,
  a,b,c,X,Y,Z for set,
  u,v,w for Element of E,
  f,g,h,i,j for Function of VAR,E;

theorem Th11:
  { x,y } misses Free H & E,f |= H implies E,f |= All(x,y,H)
proof
  assume that
A1: { x,y } misses Free H and
A2: E,f |= H;
A3: bound_in All(y,H) = y by Lm2;
  All(y,H) is universal & the_scope_of All(y,H) = H by Lm2;
  then
A4: Free All(y,H) = Free H \ { y } by A3,ZF_MODEL:1;
  x in { x,y } by TARSKI:def 2;
  then not x in Free H by A1,XBOOLE_0:3;
  then
A5: not x in Free All(y,H) by A4,XBOOLE_0:def 5;
  y in { x,y } by TARSKI:def 2;
  then not y in Free H by A1,XBOOLE_0:3;
  then E,f |= All(y,H) by A2,Th10;
  hence thesis by A5,Th10;
end;
