Mathlib Map

Theorems · Theorem · logic and foundations

ZFSet.IsTransitive.powerset

∀ {x : ZFSet.{u}}, x.IsTransitive → x.powerset.IsTransitive
Defined in
Mathlib.SetTheory.ZFC.Ordinal
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZFSet.isTransitive_vonNeumann · cited by 1ZFSet.isTransitive_vonNeu…ZFSet · cited by 259ZFSetZFSet.IsTransitive · cited by 22ZFSet.IsTransitiveZFSet.powerset · cited by 11ZFSet.powersetZFSet.mem_powerset · cited by 5ZFSet.mem_powersetZFSet.IsTransitive.subset_of_mem · cited by 4IsTransitive.subset_of_memIsTransitive.powersetCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.