theorem Th43:
  Ex(x,p '&' q) => (Ex(x,p) '&' Ex(x,q)) is valid
proof
  All(x,p '&' q => q) is valid by Lm1,Th23;
  then
A1: Ex(x,p '&' q) => Ex(x,q) is valid by Th35;
  All(x,p '&' q => p) is valid by Lm1,Th23;
  then Ex(x,p '&' q) => Ex(x,p) is valid by Th35;
  hence thesis by A1,Lm3;
end;
