reserve X for set;
reserve UN for Universe;

theorem Th72:
  FinSETS in SETS & NAT in SETS & REAL in SETS & ExtREAL in SETS
  proof
    SETS is_Tarski-Class_of FinSETS by CLASSES1:def 4;
    then
A1: omega c= FinSETS in SETS & SETS is axiom_GU1 & SETS is axiom_GU3 by Th16;
    then NAT in SETS & SETS is Grothendieck by Th13;
    then reconsider X = SETS as non trivial Universe by Def6;
    REAL is Element of X & ExtREAL is Element of X by Th53,Th54;
    hence thesis by A1,Th13;
  end;
