
theorem Th14:
for G, H being set st G c= H holds PairsOf G c= PairsOf H
proof
 let G, H be set; assume
A1: G c= H;
 let e be object;
  reconsider ee=e as set by TARSKI:1;
 assume A2: e in PairsOf G;
A3: card ee = 2 by A2,Def1;
  e in G by A2;
  hence thesis by A1,A3,Def1;
end;
