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Theorems · Theorem · logic and foundations

ZFSet.mem_vonNeumann

∀ {o : Ordinal.{u}} {x : ZFSet.{u}}, x ∈ ZFSet.vonNeumann o ↔ x.rank < o
Defined in
Mathlib.SetTheory.ZFC.VonNeumann
Cited by
2 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

ZFSet.vonNeumann_add_one · cited by 2ZFSet.vonNeumann_add_oneZFSet.mem_vonNeumann_of_subset · cited by 0ZFSet.mem_vonNeumann_of_s…le_refl · cited by 2061le_reflOrdinal · cited by 1688OrdinalLE.le.trans_lt · cited by 795le.trans_ltZFSet · cited by 259ZFSetZFSet.rank · cited by 31ZFSet.rankZFSet.vonNeumann · cited by 25ZFSet.vonNeumannZFSet.mem_vonNeumannCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.