Symbol Reference: ∃ — Existential Quantifier Binder (∃, AST Constructor: TpExis)

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∃ \(\exists\) — Existential Quantifier Binder (∃, AST Constructor: TpExis)

Primitive existential quantifier binder ∃(x:A), 𝛗 (and bounded macro ∃(x∈Y), 𝛗 ≡ ∃(x:Class), ((x∈Y)∧𝛗)).

Field Mathematical & Kernel Specification (MKTD1 / MKTD2)
Symbol
∃
\(\exists\)
Category Binder (Existential Quantifier)
SML AST Constructor HP (TpExis of (UCol * 'Truth_AFUNEX)) [in datatype Truth_p, typetheory.ML:656]
Constructor Arguments 1. Domain conglomerate A : UCol (default Class); 2. Bound variable x : Variable; 3. Body 𝛗 : Fm
Metatype / Signature (Variable : Type) × Fm → Fm
Binder Status YES — Existential Quantifier Binder (and bounded macro ∃(x∈Y),𝛗)
Defining Kernel Entries (ML Labels) See Related Symbols & Kernel Entries below.
LaTeX Form \exists
How to Understand It

SML AST Constructor: HP (TpExis of (UCol * 'Truth_AFUNEX)) in Truth_p (typetheory.ML:656). Classification: Binder. Governed by Non-emptiness of Class (AxmDiscourseNonEmpty (2.01)), Exists Introduction (RulExistsInstantiation (2.03)), and Exists Elimination/Abstraction (RulExistsAbstraction (2.05)).

Canonical Law / Usage (let x = t in 𝛗) → (∃(x:X)𝛗)
Related Symbols & Kernel Entries