Theorems · Theorem · logic and foundations
Cardinal.three_le
Deprecated since 2026-02-17Use Cardinal.exists_ne_ne_of_three_le instead.
∀ {α : Type u_1}, 3 ≤ Cardinal.mk α → ∀ (x y : α), ∃ z, z ≠ x ∧ z ≠ yAlias of Cardinal.exists_ne_ne_of_three_le.
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.exists_ne_ne_of_three_leproof · cited by 4
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