Theorems · Theorem · logic and foundations

FirstOrder.Field.FieldAxiom.toProp_of_model

∀ {K : Type u_2} [inst : Add K] [inst_1 : Mul K] [inst_2 : Neg K] [inst_3 : Zero K] [inst_4 : One K]
  [inst_5 : FirstOrder.Ring.CompatibleRing K] [K ⊨ FirstOrder.Language.Theory.field] (ax : FirstOrder.Field.FieldAxiom),
  FirstOrder.Field.FieldAxiom.toProp K ax

Defined in: Mathlib.ModelTheory.Algebra.Field.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Add Mul Neg Zero One FirstOrder.Ring.CompatibleRing FirstOrder.Language.Theory.Model

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Set.mem_range_selfproof · cited by 328
FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
FirstOrder.Language.ringstatement · cited by 36
FirstOrder.Ring.CompatibleRingstatement and proof · cited by 27
FirstOrder.Language.Theory.realize_sentence_of_memproof · cited by 11
FirstOrder.Field.FieldAxiomstatement and proof · cited by 11
FirstOrder.Language.Theory.fieldstatement and proof · cited by 6
FirstOrder.Field.FieldAxiom.toPropstatement · cited by 2
FirstOrder.Field.FieldAxiom.realize_toSentence_iff_toPropproof · cited by 1

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