what does this symbol mean (like a perpendicular symbol, in set theory)

Question

Sent from my phone so have pity on me (long train journey)

Azriel Levy basic set theory, Dover, p13

What does the symbol after the P* mean in 4.5?

Will edit in picture. Mobile mode doesn't have it.

Okay I have an answer. I will add the picture when I get home.

Thanks for not closing - I appreciate it!

Answer 1

(As the book happens to be within arm's reach as I listen to music ...)

It's the standard turnstile symbol '$\vdash$' for (syntactic) entailment.

So e.g., to simplify Levy's example, $P \vdash A \leftrightarrow B$ says that in (the theory) $P$ we can derive $A \leftrightarrow B$