
theorem Th24:
for G being SimpleGraph, x being object holds x in Vertices G iff {x} in G
proof
  let G be SimpleGraph, x be object;
  thus x in Vertices G implies {x} in G proof
    assume x in Vertices G;
    then consider y being set such that
  A1: x in y and
  A2: y in G by TARSKI:def 4;
      {x} c= y by A1,ZFMISC_1:31;
    hence {x} in G by A2,CLASSES1:def 1;
  end;
   x in {x} by TARSKI:def 1;
  hence thesis by TARSKI:def 4;
end;
