Self Doubt [closed]

Question

∀x(∀z(β)→∃y(¬α))
⟹∀x(¬∀z(β)∨∃y(¬α))
⟹¬∃x¬(¬∀z(β)∨∃y(¬α))
⟹¬∃x(∀z(β)∧¬∃y(¬α))
⟹¬∃x(∀z(β)∧∀y(α))

 

In the third line why 2 negations are used ?

Comments

$\forall xP(x)=¬¬\forall xP(x)=¬∃x¬\ P(x)$