theorem Th51:
  'not' All(x,p) => Ex(x,'not' p) is valid & Ex(x,'not' p) =>
  'not' All(x,p) is valid
proof
A1: Ex(x,'not' p) = 'not' All(x,'not' 'not' p) by QC_LANG2:def 5;
  All(x,'not' 'not' p) => All(x,p) is valid by Th45;
  hence 'not' All(x,p) => Ex(x,'not' p) is valid by A1,LUKASI_1:52;
  All(x,p) => All(x,'not' 'not' p) is valid by Th45;
  hence thesis by A1,LUKASI_1:52;
end;
