theorem Th54:
  All(x,'not' p) <=> 'not' Ex(x,p) is valid
proof
  'not' 'not' All(x,'not' p) => All(x,'not' p) is valid;
  then
A1: 'not' Ex(x,p) => All(x,'not' p) is valid by QC_LANG2:def 5;
  All(x,'not' p) => 'not' 'not' All(x,'not' p) is valid;
  then All(x,'not' p) => 'not' Ex(x,p) is valid by QC_LANG2:def 5;
  hence thesis by A1,Lm14;
end;
