Theorems · Theorem · logic and foundations
not_iff_comm
∀ {a b : Prop}, (¬a ↔ b) ↔ (¬b ↔ a)- Defined in
- Mathlib.Logic.Basic
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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 by32
Results whose statement or proof uses this declaration.
- Finsupp.notMem_support_iffproof · cited by 44
- Fintype.card_pos_iffproof · cited by 31
- not_isEmpty_iffproof · cited by 19
- DFinsupp.notMem_support_iffproof · cited by 10
- IsTranscendenceBasis.isAlgebraicproof · cited by 8
- Matroid.dual_rankPos_iff_exists_isCircuitproof · cited by 3
- finrank_vectorSpan_le_iff_not_affineIndependentproof · cited by 2
- BoxIntegral.unitPartition.disjointproof · cited by 2
- AddMonoid.exponent_eq_zero_iff_range_addOrderOf_infiniteproof · cited by 1
- Set.not_unbounded_iffproof · cited by 1
- IsSMulRegular.not_zero_iffproof · cited by 1
- LeftCancelMonoid.mul_ne_oneproof · cited by 1