reserve X,Y,x for set;
reserve A for non empty preBoolean set;

theorem Th10:
  for A, B being set st A c= B holds Fin A c= Fin B
proof
  let A,B be set;
  assume
A1: A c= B;
    let X be object;
    reconsider XX=X as set by TARSKI:1;
    assume
A2: X in Fin A;
    then XX c= A by Def5;
    then XX c= B by A1;
    hence X in Fin B by A2,Def5;
end;
