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Theorems · Theorem · logic and foundations

ZFSet.mem_powerset

∀ {x y : ZFSet.{u}}, y ∈ x.powerset ↔ y ⊆ x
Defined in
Mathlib.SetTheory.ZFC.Basic
Cited by
5 results in Mathlib
Foundations
Depth 25 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.vonNeumann_add_one · cited by 2ZFSet.vonNeumann_add_oneZFSet.isTransitive_iff_subset_powerset · cited by 1ZFSet.isTransitive_iff_su…ZFSet.IsTransitive.powerset · cited by 1IsTransitive.powersetClass.coe_powerset · cited by 0Class.coe_powersetZFSet.le_succ_rank_sUnion · cited by 0ZFSet.le_succ_rank_sUnionZFSet · cited by 259ZFSetPSet · cited by 107PSetZFSet.powerset · cited by 11ZFSet.powersetPSet.mem_powerset · cited by 2PSet.mem_powersetZFSet.subset_iff · cited by 2ZFSet.subset_iffZFSet.mem_powersetCITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.