Theorems · Theorem · logic and foundations
ZFSet.isOrdinal_iff_forall_mem_isOrdinal
∀ {x : ZFSet.{u}}, x.IsOrdinal ↔ x.IsTransitive ∧ ∀ y ∈ x, y.IsOrdinalAn ordinal is a transitive set of ordinals.
- Defined in
- Mathlib.SetTheory.ZFC.Ordinal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZFSetstatement and proof · cited by 259
- ZFSet.IsOrdinalstatement and proof · cited by 34
- ZFSet.IsTransitivestatement and proof · cited by 22
- ZFSet.IsOrdinal.isTransitiveproof · cited by 7
- ZFSet.IsOrdinal.memproof · cited by 7
- ZFSet.isOrdinal_iff_forall_mem_isTransitiveproof · cited by 1
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