theorem Th43:
  rng pr1(X,Y) c= X
proof
  let x be object;
  assume x in rng pr1(X,Y);
  then consider p being object such that
A1: p in dom pr1(X,Y) and
A2: x = pr1(X,Y).p by FUNCT_1:def 3;
  p in [:X,Y:] by A1,Def4;
  then consider x1,y1 being object such that
A3: x1 in X & y1 in Y and
A4: p = [x1,y1] by ZFMISC_1:def 2;
  x =pr1(X,Y).(x1,y1) by A2,A4;
  hence thesis by A3,Def4;
end;
