Do the page "The ZFC Axioms" contain errors? I can't understand the following proposition:

∃y∀z(∃w(z ∈ w ∧ w ∈ x) ⇒ z ∈ y)

Shouldn't it be:

∃y∀z(∃w(z ∈ w ∧ w ∈ y) ⇒ z ∈ y)