
theorem Th52:
for G being SimpleGraph, x being set st x in union G
 ex C being finite Clique of G st Vertices C = {x}
proof
 let G be SimpleGraph, x be set such that
A1: x in union G;
 set C = CompleteSGraph {x};
A2: C = { {}, {x} } by Th36;
 reconsider C as finite Clique of G by A1,A2,Th50;
 take C;
 thus Vertices C = {x} by A2,Th8;
end;
