Source: 11 mins 49 s juncture, Lecture 3-7 (transcription), ... How to Reason and Argue,
by Prof W Sinnott-Armstrong. Caution: My enumeration differs from the Prof's. For brevity, I abbreviate 'anything else that rattles when shaken' with definition 2 of the noun 'rattler'.
1. This box rattles when I shake it.
1.1. A box doesn't rattle when shaken if it contains only a sweater and not any other rattler.
Original: A box doesn't rattle when shaken if it contains only a sweater and not anything else that makes a rattling noise when shaken.
1.2. If this box contains a sweater, then it contains only a sweater, and doesn't contain any other rattler.
Original: If this box contains a sweater, then it contains only a sweater, and doesn't contain anything else that rattles when shaken.
2. So this box does not contain a sweater.
At the 9 mins 32 s juncture, the Prof did not introduce 1.3 yet (I inserted it above to save space, but apologise if it deceives). He explains that without 1.3, the argument is INVALID:
Well, no, for the same reason we saw before, because my wife might be a trickster who puts rocks around my sweater in the birthday present box, in order to fool me.
Then, the premises can be true, and the conclusion, false.
My question: Is the argument valid if we delete 1.1, and keep only and 1.2?