Theorems · Theorem · logic and foundations
not_iff_not
∀ {a b : Prop}, (¬a ↔ ¬b) ↔ (a ↔ b)- Defined in
- Mathlib.Logic.Basic
- Cited by
- 159 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 51 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by159
Results whose statement or proof uses this declaration.
- abs_eq_zeroproof · cited by 17
- Filter.HasBasis.disjoint_iffproof · cited by 13
- Nat.finiteMultiplicity_iffproof · cited by 13
- Unitization.quasispectrum_eq_spectrum_inr'proof · cited by 12
- Cardinal.mk_ne_zero_iffproof · cited by 11
- IsLocalRing.local_hom_TFAEproof · cited by 10
- map_eq_zeroproof · cited by 10
- IsLocalization.AtPrime.to_map_mem_maximal_iffproof · cited by 9
- IsLocalRing.isField_iff_maximalIdeal_eqproof · cited by 8
- Finset.one_lt_card_iff_nontrivialproof · cited by 6
- Set.isEmpty_coe_sortproof · cited by 6
- NumberField.InfinitePlace.isUnramified_iffproof · cited by 6