Theorems · Theorem · logic and foundations
by_contra
∀ {p : Prop}, (¬p → False) → pAlias of by_contradiction.
- Defined in
- Mathlib.Logic.Basic
- Cited by
- 60 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.
- by_contradictionproof · cited by 42
Cited by60
Results whose statement or proof uses this declaration.
- of_not_notproof · cited by 51
- isPurelyInseparable_iff_pow_memproof · cited by 10
- Matroid.IsBasis.mem_of_insert_indepproof · cited by 9
- BoxIntegral.Prepartition.eq_of_mem_of_memproof · cited by 6
- Set.encard_lt_top_iffproof · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- exists_linearIndepOn_extensionproof · cited by 5
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- MvPowerSeries.eq_of_coeff_monomial_ne_zeroproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Set.minimal_iff_forall_sdiff_singletonproof · cited by 3