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Theorems · Theorem · logic and foundations

FirstOrder.Language.Formula.realize_iff

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {α : Type u'} {φ ψ : L.Formula α} {v : α → M},
  (φ.iff ψ).Realize v ↔ (φ.Realize v ↔ ψ.Realize v)
Defined in
Mathlib.ModelTheory.Semantics
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.Structure
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FirstOrder.Language.Sentence.realize_iff · cited by 0Sentence.realize_iffFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Formula · cited by 93Language.FormulaFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFirstOrder.Language.BoundedFormula.realize_iff · cited by 7BoundedFormula.realize_iffFirstOrder.Language.Formula.iff · cited by 2Formula.iffFormula.realize_iffCITED BYCITES

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