Theorems · Theorem · logic and foundations
ZFSet.IsOrdinal.subset_iff_eq_or_mem
∀ {x y : ZFSet.{u}}, x.IsOrdinal → y.IsOrdinal → (x ⊆ y ↔ x = y ∨ x ∈ y)- Defined in
- Mathlib.SetTheory.ZFC.Ordinal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- le_reflproof · cited by 2,061
- Sym2.mkproof · cited by 332
- ZFSetstatement and proof · cited by 259
- subset_antisymmproof · cited by 150
- ZFSet.IsOrdinalstatement and proof · cited by 34
- WellFounded.has_minproof · cited by 26
- Sym2.GameAddproof · cited by 14
- Set.notMem_of_mem_sdiffproof · cited by 9
- ZFSet.IsOrdinal.memproof · cited by 7
- Sym2.GameAdd.recursionproof · cited by 5
- Set.sdiff_nonemptyproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- ZFSet.IsOrdinal.eq_or_mem_of_subsetproof · cited by 1
- ZFSet.IsOrdinal.mem_trichotomousproof · cited by 1