Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.Iff.all
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} {φ ψ : L.BoundedFormula α (n + 1)},
T.Iff φ ψ → T.Iff φ.all ψ.all- Defined in
- Mathlib.ModelTheory.Equivalence
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- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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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.Theory.ModelTypeproof · cited by 62
- FirstOrder.Language.Theory.ModelType.Carrierproof · cited by 59
- FirstOrder.Language.Theory.Iffstatement and proof · cited by 32
- FirstOrder.Language.Theory.Iff.realize_bd_iffproof · cited by 5
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