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#2059489 ·published 2011-05-14 20:05 UTC
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𝒜 ⊨ ¬∃xF ⇔ ¬∃a ∈ A  𝒜[x→a] (F) = 1 ⇔ ∀a ∈ A  𝒜[x→a] (F) = 0
𝒜 ⊨ ∃x¬F ⇔ ∃a ∈ A  𝒜[x→a](F) = 0