Theorems · Theorem · logic and foundations
Function.mt
∀ {a b : Prop}, (a → b) → ¬b → ¬aProvide modus tollens (mt) as dot notation for implications.
- Defined in
- Mathlib.Logic.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
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 by27
Results whose statement or proof uses this declaration.
- Ideal.map_ne_bot_of_ne_botproof · cited by 7
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- minpoly.ne_zero_iffproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- hasFiniteSupport_of_finsum_ne_zeroproof · cited by 2
- FormalMultilinearSeries.ofScalars_eq_zeroproof · cited by 2
- SimpleGraph.reachable_of_edist_ne_topproof · cited by 2
- MulChar.apply_ne_zero_iffproof · cited by 2
- Finset.coe_infsepproof · cited by 2
- hasFiniteMulSupport_of_finprod_ne_oneproof · cited by 1
- IsLocalRing.maximalIdeal_sq_lt_of_ringKrullDim_ne_zeroproof · cited by 1