Theorems · Theorem · logic and foundations
existsUnique_of_exists_of_unique
∀ {α : Sort u_1} {p : α → Prop}, (∃ x, p x) → (∀ (y₁ y₂ : α), p y₁ → p y₂ → y₁ = y₂) → ∃! x, p x- Defined in
- Mathlib.Logic.ExistsUnique
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ExistsUniquestatement · cited by 268
- ExistsUnique.introproof · cited by 5
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.isContinuous_of_coverPreservingproof · cited by 4
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernelproof · cited by 3
- CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernelproof · cited by 3
- Set.PairwiseDisjoint.isPartition_of_exists_of_ne_emptyproof · cited by 2
- Submodule.existsUnique_from_graphproof · cited by 2
- SSet.S.existsUnique_nproof · cited by 2
- SSet.N.existsUnique_of_leproof · cited by 2
- Localization.existsUnique_algebraMap_eq_of_span_eq_topproof · cited by 1
- CategoryTheory.ObjectProperty.IsDetecting.isIso_iff_of_monoproof · cited by 1
- SSet.S.existsUnique_toNπproof · cited by 1
- Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zeroproof · cited by 1