@JackVassau "[things that] should be provided, then..." is the necessary condition for the "things necessary for human health", not for the "primary purpose" condition. Just like B is not a necessary condition for C in A -> B -> C. Note that it reads if A, then if (!) B, then C.

When we kick "things necessary for human health" up to the domain, "then" before "[things that] should be provided" is removed along with the starting "if", just like "then" will be removed before B if we kick A up into the domain and are left with B -> C (if B, then C).

"So such wounds is a reference to deep wounds free of bacteria." (0:50 mark in the video) is a false statement. "Such wounds" refers to "deep wounds".

If we swap out the referential in the second sentence by the referent as suggested in the video, the resulting sentence will make no sense: "Even strong antibiotics failed to kill the bacteria that live in deep wounds free of bacteria."