Is this the correct way to quantify these integers?

[Math100]

TL;DR

I just have this random question and I was wondering if the following quantifier below is correct to represent/symbolize nonzero integers $a, b, c, d$:
$\forall a, b, c, d\in\mathbb{Z}_{\neq 0}$

Does the above quantifier represent/symbolize that all of the integers $a, b, c, d$ cannot be $0$? Is this correct?

 

[andrewkirk]

It is non-standard, but all that really matters is that the reader understands what you mean. I think they will.
If you want to write it perfectly correctly you could write:
$$\forall a,b,c,d\in \mathbb Z - \{0\}$$

 

[topsquark]

TL;DR Summary: I just have this random question and I was wondering if the following quantifier below is correct to represent/symbolize nonzero integers $a, b, c, d$:
$\forall a, b, c, d\in\mathbb{Z}_{\neq 0}$

Does the above quantifier represent/symbolize that all of the integers $a, b, c, d$ cannot be $0$? Is this correct?

Or, perhaps $\{ a, b, c, d \} \subset \mathbb{Z} - \{ 0 \}$

-Dan

 

[Math100]

Thank you for the clarification, @andrewkirk @topsquark .