theorem
  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 Th32;
  hence thesis by A1,CQC_THE1:65;
end;
