Theorems · Theorem · logic and foundations
ZFSet.IsTransitive.subset_powerset
∀ {x : ZFSet.{u}}, x.IsTransitive → x ⊆ x.powersetAlias of the forward direction of ZFSet.isTransitive_iff_subset_powerset.
- Defined in
- Mathlib.SetTheory.ZFC.Ordinal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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Cites4
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.IsTransitivestatement · cited by 22
- ZFSet.powersetstatement · cited by 11
- ZFSet.isTransitive_iff_subset_powersetproof · cited by 1
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