reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;
reserve U1,U2,U for Universe;

theorem Th61:
  X in U & Y in U implies [:X,Y:] in U & Funcs(X,Y) in U
proof
  assume that
A1: X in U and
A2: Y in U;
  X \/ Y in U by A1,A2,Th60;
  then bool(X \/ Y) in U by Th59;
  then
A3: bool bool(X \/ Y) in U by Th59;
  [:X,Y:] c= bool bool(X \/ Y) by ZFMISC_1:86;
  hence [:X,Y:] in U by A3,CLASSES1:def 1;
  then
A4: bool [:X,Y:] in U by Th59;
  Funcs(X,Y) c= bool [:X,Y:] by FRAENKEL:2;
  hence thesis by A4,CLASSES1:def 1;
end;
