reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem Th116:
  for G being _Graph holds (ex v1, v2 being Vertex of G st v1 <> v2)
    implies G is non _trivial
proof
  let G be _Graph;
  given v1, v2 being Vertex of G such that
    A1: v1 <> v2;
  card the_Vertices_of G <> 1
  proof
    assume card the_Vertices_of G = 1;
    then card {v1,v2} c= 1 by CARD_1:11;
    then {0,1} c= 1 by A1, CARD_2:57, CARD_1:50;
    then 1 in 1 by ZFMISC_1:32;
    hence contradiction;
  end;
  hence thesis;
end;
