Negation of quantified statements (Flip ∀↔∃ and negate the predicate; negation passes through quantifiers)

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Flip ∀↔∃ and negate the predicate; negation passes through quantifiers with swap

What each symbol means

SymbolWhat it stands for
xVariable over stated domain
P(x)Predicate

When to use this

Classical first-order negation as in JEE.