I couldn't figure out where else to post this so here it is. I'm working through my lecture notes for my analytical statistics course, currently covering the topics of convergence in probability and distribution, and then this comes up. Spoiler: Picture Is there even a possibility that this proof is valid given that the second line uses a result as a condition??? I've done some googling and I've found nothing so far that even comes close to following this process. Normally I would just "oh that's a bad proof, whoever wrote it is wrong". But this is my statistics lecturer who has a doctorate in the subject and for a lecture for an accredited university so like? There has to be something that I'm missing, right? Edit: changed professor to lecturer because I continue to forget that they are not the same person.