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closed with the note: Cleared

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

 

In the third line why 2 negations are used ?

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Is this statement valid:$(\exists x(P(x)\rightarrow Q(x)) )\rightarrow (\exists xP(x)\rightarrow \exists xQ(x))$