
theorem Th98:
for G being SimpleGraph, x, y being object
 st x <> y holds not {[x,union G],[y,union G]} in Mycielskian G
proof
  let G be SimpleGraph, x, y be object such that
A1: x <> y and
A2: {[x,union G],[y,union G]} in Mycielskian G;
   [x,union G] <> [y,union G] by A1,XTUPLE_0:1;
   then card {[x,union G],[y,union G]} = 2 by CARD_2:57;
   then {[x,union G],[y,union G]} in Edges Mycielskian G by A2,Def1;
  hence contradiction by Th97;
end;
