
theorem Th3:
  for a, b being set holds a is Subset of b iff a c= b
proof
  let a, b be set;
  hereby
    assume a is Subset of b;
    then a in bool b by SUBSET_1:def 1;
    hence a c= b by ZFMISC_1:def 1;
  end;
  assume a c= b;
  then a in bool b by ZFMISC_1:def 1;
  hence thesis by SUBSET_1:def 1;
end;
