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Theorems · Theorem · logic and foundations

ZFSet.isOrdinal_iff_forall_mem_isTransitive

∀ {x : ZFSet.{u}}, x.IsOrdinal ↔ x.IsTransitive ∧ ∀ y ∈ x, y.IsTransitive

An ordinal is a transitive set of transitive sets.

Defined in
Mathlib.SetTheory.ZFC.Ordinal
Cited by
1 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Quot.sound
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Around this declaration

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ZFSet.isOrdinal_iff_forall_mem_isOrdinal · cited by 0ZFSet.isOrdinal_iff_foral…ZFSet · cited by 259ZFSetZFSet.IsOrdinal · cited by 34ZFSet.IsOrdinalZFSet.IsTransitive · cited by 22ZFSet.IsTransitiveZFSet.IsOrdinal.isTransitive · cited by 7IsOrdinal.isTransitiveZFSet.IsOrdinal.mem · cited by 7IsOrdinal.memZFSet.IsTransitive.mem_trans · cited by 7IsTransitive.mem_transZFSet.isOrdinal_iff_forall_me…CITED BYCITES

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