Self Doubt
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in Mathematical Logic closed by
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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 ?

in Mathematical Logic closed by
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$\forall xP(x)=¬¬\forall xP(x)=¬∃x¬\ P(x)$
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