theorem Th23:
  x in rng p implies x..p in p " {x}
proof
  assume
A1: x in rng p;
  then p.(x..p) = x by Th19;
  then
A2: p.(x..p) in {x} by TARSKI:def 1;
  x..p in dom p by A1,Th20;
  hence thesis by A2,FUNCT_1:def 7;
end;
