case def_exists_ v phi =>
  intro D I V E _
  simp only [Holds]
  simp
Δ : List Formula
F : Formula
v : VarName
phi : Formula
⊢ ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H ∈ [], Holds D I V E H) → Holds D I V E ((exists_ v phi).iff_ (forall_ v phi.not_).not_)
no goals