
theorem Th62:
for G being SimpleGraph, x, y being set
 st x in Vertices G & y in Vertices G & {x,y} nin G
  holds {x, y} is StableSet of G
proof
 let G be SimpleGraph, x, y be set such that
A1: x in Vertices G and
A2: y in Vertices G and
A3: {x,y} nin G;
   reconsider S = {x,y} as Subset of Vertices G by A1,A2,ZFMISC_1:32;
  S is stable proof
   let a, b be set such that
  A4: a <> b and
  A5: a in S and
  A6: b in S;
      (a = x or a = y) & (b = x or b = y) by A5,A6,TARSKI:def 2;
   hence {a,b} nin G by A3,A4;
  end;
  hence {x, y} is StableSet of G;
end;
