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Theorems · Theorem · logic and foundations

PSet.mem_powerset

∀ {x y : PSet.{u_1}}, y ∈ x.powerset ↔ y ⊆ x
Defined in
Mathlib.SetTheory.ZFC.PSet
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
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Around this declaration

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

ZFSet.mem_powerset · cited by 5ZFSet.mem_powersetPSet.le_succ_rank_sUnion · cited by 0PSet.le_succ_rank_sUnionSet.Elem · cited by 7166Set.ElemSet.ofPred · cited by 6101Set.ofPredPSet · cited by 107PSetPSet.Equiv · cited by 44PSet.EquivPSet.Type · cited by 34PSet.TypePSet.Func · cited by 29PSet.FuncPSet.Equiv.refl · cited by 5Equiv.reflPSet.powerset · cited by 2PSet.powersetPSet.Subset.congr_left · cited by 1Subset.congr_leftPSet.mem_powersetCITED BYCITES

Cites9

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.