theorem Th31:
  All(x,p => q) is valid implies All(x,p) => All(x,q) is valid
proof
  assume
A1: All(x,p => q) is valid;
  All(x,p => q) => (All(x,p) => All(x,q)) is valid by Th30;
  hence thesis by A1,CQC_THE1:65;
end;
