theorem Th25:
  p=h.x & q=h.y & not x in still_not-bound_in h implies All(x,p) => q is valid
proof
  assume that
A1: p=h.x and
A2: q=h.y and
A3: not x in still_not-bound_in h;
A4: (All(x,p) => h).y = (All(x,p).y) => q by A2,Th12
    .= All(x,p) => q by CQC_LANG:27;
  not x in still_not-bound_in All(x,p) by Th5;
  then
A5: All(x,p) => p is valid & not x in still_not-bound_in All(x,p) => h by A3
,Th7,CQC_THE1:66;
  (All(x,p) => h).x = (All(x,p).x) => p by A1,Th12
    .= All(x,p) => p by CQC_LANG:27;
  hence thesis by A4,A5,CQC_THE1:68;
end;
