Propositional logic without set theory

Hello, I am new in this forum.

I have a question regarding propositional logic: after having studied physics, now in my free time I am coming back a second time and I am trying to study mathematics properly, as a pleasure.

I want to start with logic, study well the "language of mathematics", and then proceed towards set theory and then to study properly analysis and other subjects of my interest (understanding quantum field theory correctly, at the mathematical level of rigor, is my target).

But I find a surprising problem: in all the books I am checking of logic (mathematical logic) they use the concept of a set beforehand, even though logic has to be the basis of a language for all mathematics, where even set theory has to be based on!

Of course, I understand that it is not the same axiomatic set theory than naive set theory. And talking about sets is not saying really anything, more than "the grouping of a few concepts", but it bothers me.

Even some books use concepts like "smallest set" without defining it.

And I am talking about "classic" books, like Mendelson, Hinman, Hedman or Shoenfield.

Could anybody give me a suggestion of a book on propositional logic that does not use set theory at all, but it gives a full preparation for axiomatic set theory? Ideally, I would like a modern book, because I like modern notation (I do not like old books, with cumbersome notations ... I know this should not be essential for a correct understanding, but it is the way I feel).

My plan is to study afterwards the book of Jech on Set Theory.