reserve X for set;
reserve UN for Universe;

theorem Th78:
  for X being non empty set
  for GX being Grothendieck of X
  for G being Universe st X misses G
  holds GX <> G
  proof
    let X be non empty set;
    let GX be Grothendieck of X;
    let G be Universe;
    assume
A1: X misses G;
    assume GX = G;
    then X in G & G is axiom_GU1 & G is axiom_GU3 by CLASSES3:def 4;
    then X c= G;
    hence thesis by A1,XBOOLE_1:68;
  end;
