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Theorems · Theorem · logic and foundations

and_forall_ne

∀ {α : Sort u_1} {p : α → Prop} (a : α), (p a ∧ ∀ (b : α), b ≠ a → p b) ↔ ∀ (b : α), p b
Defined in
Mathlib.Logic.Basic
Cited by
6 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Function.forall_update_iff · cited by 12Function.forall_update_iffBoxIntegral.Box.coe_splitLower · cited by 4Box.coe_splitLowerBoxIntegral.Box.coe_splitUpper · cited by 4Box.coe_splitUpperWithZeroTopology.isOpen_iff · cited by 1WithZeroTopology.isOpen_i…continuousOn_update_iff · cited by 1continuousOn_update_iffAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.prime · cited by 0asIdeal.primeDecidable.and_forall_ne · cited by 2Decidable.and_forall_neand_forall_neCITED BYCITES

Cites1

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

Cited by6

Results whose statement or proof uses this declaration.