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Theorems · Theorem · logic and foundations

FirstOrder.Language.Theory.Imp.trans

∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {n : ℕ} {φ ψ θ : L.BoundedFormula α n},
  T.Imp φ ψ → T.Imp ψ θ → T.Imp φ θ
Defined in
Mathlib.ModelTheory.Equivalence
Cited by
2 results in Mathlib
Foundations
Depth 23 from the axioms · uses no axioms
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FirstOrder.Language.Theory.imp_inf_iff · cited by 0Theory.imp_inf_iffFirstOrder.Language.Theory.sup_imp_iff · cited by 0Theory.sup_imp_iffFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.BoundedFormula · cited by 207Language.BoundedFormulaFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Theory.ModelType · cited by 62Theory.ModelTypeFirstOrder.Language.Theory.ModelType.Carrier · cited by 59ModelType.CarrierFirstOrder.Language.Theory.Imp · cited by 16Theory.ImpImp.transCITED BYCITES

Cites6

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Cited by2

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