
theorem Th17:
for X being set st X is void holds PairsOf X = {}
proof
  let G be set such that
A1: G is void;
  assume PairsOf G <> {};
  then consider x being object such that
A2: x in PairsOf G by XBOOLE_0:def 1;
   reconsider x as set by TARSKI:1;
A3: card x = 2 by A2,Def1;
   G = {{}} by A1;
   then x = {} by A2,TARSKI:def 1;
  hence thesis by A3;
end;
