reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;

theorem Th3:
  x in dom p implies p.x = TRUE or p.x = FALSE
  proof
    assume that
A1: x in dom p;
A2: rng p c= BOOLEAN by RELAT_1:def 19;
    p.x in rng p by A1,FUNCT_1:3;
    hence thesis by A2,TARSKI:def 2;
  end;
