2 votes 2 votes closed with the note: Cleared ∀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 ? Mathematical Logic first-order-logic + – Shamim Ahmed asked Dec 23, 2018 closed Dec 23, 2018 by Shamim Ahmed Shamim Ahmed 264 views comment Share Follow See 1 comment See all 1 1 comment reply Shobhit Joshi commented Dec 23, 2018 reply Follow Share $\forall xP(x)=¬¬\forall xP(x)=¬∃x¬\ P(x)$ 3 votes 3 votes Please log in or register to add a comment.