Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.iff_iff_imp_and_imp
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} {φ ψ : L.BoundedFormula α n},
T.Iff φ ψ ↔ T.Imp φ ψ ∧ T.Imp ψ φ- Defined in
- Mathlib.ModelTheory.Equivalence
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.BoundedFormulastatement and proof · cited by 207
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.BoundedFormula.Realizeproof · cited by 104
- FirstOrder.Language.Theory.ModelTypeproof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.Theory.Iffstatement · cited by 32
- FirstOrder.Language.Theory.Impstatement · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.Theory.imp_antisymmproof · cited by 0
- FirstOrder.Language.Theory.Iff.mpproof · cited by 0
- FirstOrder.Language.Theory.Iff.mprproof · cited by 0