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Theorems · Theorem · logic and foundations

ZFSet.IsTransitive.mem_trans

∀ {z : ZFSet.{u}}, z.IsTransitive → ∀ {x y : ZFSet.{u}}, x ∈ y → y ∈ z → x ∈ z

Alias of the forward direction of ZFSet.isTransitive_iff_mem_trans.

Defined in
Mathlib.SetTheory.ZFC.Ordinal
Cited by
7 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ZFSet.IsOrdinal.mem_trans · cited by 4IsOrdinal.mem_transZFSet.isOrdinal_iff_isTrans · cited by 3ZFSet.isOrdinal_iff_isTra…ZFSet.IsTransitive.sUnion' · cited by 2IsTransitive.sUnion'ZFSet.isTransitive_iff_sUnion_subset · cited by 1ZFSet.isTransitive_iff_sU…ZFSet.isOrdinal_iff_forall_mem_isTransitive · cited by 1ZFSet.isOrdinal_iff_foral…ZFSet.IsTransitive.inter · cited by 0IsTransitive.interZFSet.IsTransitive.sUnion · cited by 0IsTransitive.sUnionZFSet · cited by 259ZFSetZFSet.IsTransitive · cited by 22ZFSet.IsTransitiveZFSet.isTransitive_iff_mem_trans · cited by 1ZFSet.isTransitive_iff_me…IsTransitive.mem_transCITED BYCITES

Cites3

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

Cited by7

Results whose statement or proof uses this declaration.