We can prove that a buyer is פטור from חלה.
The Mishna in Challah [1-3] says:
"אלו חייבין בחלה ופטורין מן המעשרות הלקט והשכחה והפאה וההפקר וכו'"
When listing the produce that is חייב in חלה and פטור from מעשר the Mishna significantly OMITS a buyer. So it must be that a buyer is פטור from חלה.
However we can reject this because the Mishna Rishona already asked why the Mishna doesn't also enumerate תבואה that wasn't רואה פני הבית - didn't come into the house?
He answered that since מעשר is also חייב מדרבנן before it enters the house, it was not listed. Since bought produce is also חייב מדרבנן במעשר, it makes sense that it also wasn't listed. So there is no proof from the omission that a buyer is פטור from חלה.
Lots more to come I hope!😊
[We should really have a post as to whether a buyer is חייב in Schlissel Challah].
