Quantifiers for all x,y in R

Question

Can I write

$$\forall{ x, y \in{\mathbb{R}}}$$

Instead of

$$\forall{ x \in{\mathbb{R}}} \, \forall{ y \in{\mathbb{R}}}$$

Since it is much shorter and a similar notation is usually used in sets?

Answer 1

Yes, you can. In fact it is much more usual to write $\forall x,y\in\mathbb R$ than $\forall x\in\mathbb R\,\forall y\in\mathbb R$.