
theorem Th12:
for X being set, x, y being object st x <> y & {x, y} in X
holds {x, y} in PairsOf X
proof
 let X be set, x, y be object such that
A1: x <> y and
A2: {x, y} in X;
  card {x,y} = 2 by A1,CARD_2:57;
 hence {x, y} in PairsOf X by A2,Def1;
end;
