. intro h;
  replace h : p ∉ Ω.theory ∨ q ∈ Ω.theory := or_iff_not_imp_left.mpr (by simpa using h);
  cases h with
  | inl h =>
    apply membership_iff.mpr;
    exact efq_of_neg! $ membership_iff.mp $ iff_mem_neg.mpr h;
  | inr h =>
    apply membership_iff.mpr;
    exact imply₁! ⨀ (membership_iff.mp h)
case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
Ω Ω₁ Ω₂ : MCT L
p q : Formula α
⊢ (p ∈ Ω.theory → q ∈ Ω.theory) → p ⟶ q ∈ Ω.theory
no goals