Order of operators in Logic

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I was solving one question and came across the below expression

$\{ \forall x, \alpha \rightarrow (\exists y, \beta \rightarrow (\forall u, \exists v, y) \}$

My query was, that does the comma here means the below expression?

$\{ \forall x( \alpha \rightarrow (\exists y(\beta \rightarrow (\forall u, \exists v, y))) \}$