Q:

Why does "unless" mean "if not"?

Harry Gensler. Introduction to Logic (2017 3 ed). p 169.

“Unless” is also equivalent to “if not”; so we also could use “(∼B ⊃ D) (“If you
don’t breathe, then you’ll die”).”

Nicholas JJ Smith, Logic: The Laws of Truth (2012). p 115.

The statement “P unless Q” means that if Q is not true, P is true—so we
translate it as $¬ \, Q→P$.

Using solely the original meaning of "unless" below, please expound why? How does definition 1 below $\equiv$ if not?  OED Third Edition, June 2017. Screenshot.

†A. adv. Only in conjunctional phrases followed by than or that.

Forming a conjunctional phrase introducing a case in which an exception to a preceding negative statement (expressed or implied) will or may exist: (not) on a less or lower condition, requirement, etc., than (what is specified). Obsolete.

A:

This is probably too long for a comment.
First, “$p$ unless $q$” is explained in your first link as “if not $q$, then $p$”, which seems exactly right to me.
As for dictionary definitions, my American Heritage Dictionary says, “except on the condition that”, in other words, that $p$ will be the case at all times, the only possible exceptions occurring when $q$ holds.
To my mind, the two say the same thing.

