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Theorems · Theorem · logic and foundations

ZFSet.exists_mem_vonNeumann

∀ (x : ZFSet.{u_1}), ∃ o, x ∈ ZFSet.vonNeumann o

Every set is in some element of the von Neumann hierarchy.

Defined in
Mathlib.SetTheory.ZFC.VonNeumann
Cited by
1 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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ZFSet.iUnion_vonNeumann · cited by 0ZFSet.iUnion_vonNeumannOrdinal · cited by 1688OrdinalOrder.succ · cited by 633Order.succZFSet · cited by 259ZFSetZFSet.rank · cited by 31ZFSet.rankZFSet.vonNeumann · cited by 25ZFSet.vonNeumannZFSet.mem_vonNeumann_succ · cited by 1ZFSet.mem_vonNeumann_succZFSet.exists_mem_vonNeumannCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.