Two men were about to enter a beis hamedrash, one is wearing his tallis and tefillin, and the other is carrying them in his hand. Who is given precedence to enter first?

The question was presented to the Beis Halevi who said that the latter one takes precedence.

The Mishna says in Negaim, that if one enters a house that had been afflicted by tzaraas, he becomes tamei. If he is carrying clothes on his shoulders, they too became tamei instantly. Howeer, if he was wearing the clothes, they do not fit into the passuk which says that "anything that comes into the house shall be tamei," and thus do not instantly become tamei. (See Negaim 13.9 for more details).

The Beis Halevi deduced from here, that if one is wearing tefillin they are considered part of one's body, but if one is carrying them they are considered an independent item, and therefore the person who was carrying the tefillin – an article of kedusha – must enter the room first.