
theorem Th8:
  for X, x being set holds x in Dependencies X iff ex a, b being
  Subset of X st x = [a,b]
proof
  let X be set, x be set;
  hereby
    assume
A1: x in Dependencies X;
    then consider a, b being object such that
A2: [a, b] = x by RELAT_1:def 1;
    reconsider a, b as Subset of X by A1,A2,ZFMISC_1:87;
    take a,b;
    thus x = [a,b] by A2;
  end;
  given a, b being Subset of X such that
A3: x = [a,b];
  thus thesis by A3,ZFMISC_1:87;
end;
