I am writing a mathematics paper with the intent to publish it in a peer-review journal. I have written something along the lines of
Theorem 2.
(1) something
(2) something else.
(end of Theorem 2).
Then later in the paper, I write (my attempt)
$$f(x) \hspace{0.2cm}\begin{array}{ll} >0 & \mbox{always $\iff$ Thm. 2 (1) $\land$ (2)};\\ <0 & \mbox{if Thm. 2 $\neg$(1) $\lor$ $\neg$(2)}.\end{array} $$ What I am trying to say is this (I do not have enough room and am looking for something more concise):
$$f(x) \hspace{0.2cm}\begin{array}{ll} >0 & \mbox{for all x if and only if both Theorem 2. (1) and Theorem 2. (2) are true };\\ <0 & \mbox{if either Theorem 2. (1) or Theorem 2. (2) is not true}.\end{array} $$
Was my attempt correct? acceptable for a peer-review journal?
I think your notation is too cryptic. It's not clear whether the word "always" in the first line applies to the preceding inequality (namely, $f(x) > 0$) or to the following logical symbol (namely, the $\iff$ symbol). In the second line, it's not clear whether you're saying that $f(x) < 0$ for some $x$ or for all $x$. It's also hard for me to imagine what Theorem 2 could possibly look like in order to make "$\mbox{Thm. 2 (1) $\land$ (2)}$" meaningful.
And besides that, this notation just isn't standard or well-known. You shouldn't use non-standard notation without a good reason, and you should never use non-standard notation without explaining exactly what it means.
Math is hard to understand even when it's well-written. Don't make the problem even worse by using unclear notation.
Just use prose instead: