Theorems · Theorem · logic and foundations
Function.mtr
∀ {a b : Prop}, (¬a → ¬b) → b → aProvide the reverse of modus tollens (mt) as dot notation for implications.
- Defined in
- Mathlib.Logic.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- not_imp_notproof · cited by 63
Cited by12
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.leadingCoeff_eq_zeroproof · cited by 9
- Fin.find_le_of_posproof · cited by 4
- Polynomial.natSepDegree_eq_zero_iffproof · cited by 3
- MvPolynomial.esymmAlgHom_fin_injectiveproof · cited by 2
- Subspace.dualAnnihilator_dualCoannihilator_eqproof · cited by 2
- zero_mem_asymptoticConeproof · cited by 2
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- Polynomial.nodup_roots_iff_of_splitsproof · cited by 1
- asymptoticCone_nonemptyproof · cited by 1
- LinearMap.dualMap_injective_iffproof · cited by 1
- linearIndependent_powproof · cited by 0
- Ordinal.isInitial_succproof · cited by 0