What are standard ways to write mathematical expressions involving quantifiers in a (semi)formal way ? In different posts of mine concerning similar question I have encountered for a generic expression of the type "for all $x\in I$ and $y\in J$ holds $P(x,y)$" the following writing conventions
1) $\forall y\in J \ \ \forall x \in I: P(x,y)$ (this was how I would usually write statements in a formal way; sometimes also as $\forall y\in J: \ \ \forall x \in I: P(x,y)$ ;don't know if it standard)
2) $(\forall y)(\forall x)(x \in I \land y\in J \Rightarrow P(x,y))$ (in the accepted answer from this question)
3) $(\forall y: \ y \in J) (\forall x: \ x \in I) (P(x,y))$ (form the same answer as above)
4) $\forall y \ \forall x\ (x \in I \land y \in J \Rightarrow P(x,y))$ (in the accepted answer fromthis question)
5) $(\forall y\in J )(\forall x \in I) [P(x,y)] $ (in the accepted answer from this question).
( (I hope I "generalised" them correctly, because at some points, they where written only for one variable, for example 3) was written just as $(\forall x: \ x \in I) (P(x))$ )
Could you tell me which ones are generally accepted an if there is a standard to how these should be written ?
(I think unique readability should be a criterion and I'm not sure the way I'm used to writing mathematical expression satisfies that)