⟷ \(\leftrightarrow\) — Logical Equivalence Connective (⟷, AST Constructor: TpIff)
Binary bi-implication connective 𝛂 ⟷ 𝛃 asserting logical equivalence of two propositions.
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
⟷
\(\leftrightarrow\)
|
| Category | Logical Connective (Binary Truth-Functional Symbol) |
| SML AST Constructor | HP (TpIff of ('Truth_EXP * 'Truth_EXP)) [in datatype Truth_p, typetheory.ML:652] |
| Constructor Arguments | 1. Left formula 𝛂 : Fm; 2. Right formula 𝛃 : Fm |
| Metatype / Signature | Fm × Fm → Fm | Bool × Bool → Bool |
| Binder Status | No — Binary Logical Connective (Logical Equivalence) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \leftrightarrow |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | (𝛂 ⟷ 𝛃) ⟷ ((𝛂 → 𝛃) ∧ (𝛃 → 𝛂)) |
| Related Symbols & Kernel Entries |