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Theorems · Theorem · logic and foundations

Iff.ne

∀ {α : Sort u_1} {β : Sort u_2} {a b : α} {c d : β}, (a = b ↔ c = d) → (a ≠ b ↔ c ≠ d)
Defined in
Mathlib.Logic.Basic
Cited by
52 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
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Around this declaration

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

Finset.card_ne_zero · cited by 5Finset.card_ne_zeroHahnEmbedding.Partial.orderTop_eq_archimedeanClassMk · cited by 3Partial.orderTop_eq_archi…Valuation.IsEquiv.valueGroup₀Fun_spec · cited by 3IsEquiv.valueGroup₀Fun_sp…enorm_ne_zero · cited by 3enorm_ne_zeroRat.cast_ne_zero · cited by 3Rat.cast_ne_zeroDyckWord.toList_ne_nil · cited by 3DyckWord.toList_ne_nilSimpleGraph.edist_pos_of_ne · cited by 3SimpleGraph.edist_pos_of_…Valuation.IsEquiv.orderMonoidIso_spec · cited by 2IsEquiv.orderMonoidIso_sp…Valuation.IsEquiv.pos_iff · cited by 2IsEquiv.pos_iffOrthogonalIdempotents.option · cited by 2OrthogonalIdempotents.opt…Valuation.IsEquiv.uniformContinuous_equiv · cited by 2IsEquiv.uniformContinuous…SimpleGraph.edgeSet_nonempty · cited by 2SimpleGraph.edgeSet_nonem…Pi.single_ne_zero_iff · cited by 2Pi.single_ne_zero_iffPolynomial.degree_smul_of_isRightRegular_leadingCoeff · cited by 2Polynomial.degree_smul_of…Module.FaithfullyFlat.of_comap_surjective · cited by 2FaithfullyFlat.of_comap_s…Iff.not · cited by 489Iff.notIff.neCITED BYCITES

Cites1

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

Cited by52

Results whose statement or proof uses this declaration.