theorem Th18:
  F in UFilter BL.a iff F is being_ultrafilter & a in F
proof
  hereby
    assume F in UFilter BL.a;
    then ex F0 st ( F0=F)&( F0 is being_ultrafilter)&( a in F0) by Th17;
    hence F is being_ultrafilter & a in F;
  end;
  thus thesis by Th17;
end;
