. intro h;
  exact disj₃'!
    (implyOrLeft'! $ implyOrLeft'! imp_id!)
    (by
      apply provable_iff_provable.mpr;
      apply deduct_iff.mpr;
      exact disj₃'! (implyOrLeft'! $ implyOrRight'! imp_id!) (implyOrRight'! imp_id!) id!;
    )
    h;
case mp
F : Type u_1
inst✝⁴ : LogicalConnective F
inst✝³ : DecidableEq F
S : Type u_2
inst✝² : System F S
𝓢 : S
inst✝¹ : Minimal 𝓢
p q r : F
Γ Δ : List F
inst✝ : System.NegationEquiv 𝓢
⊢ 𝓢 ⊢! p ⋎ q ⋎ r → 𝓢 ⊢! (p ⋎ q) ⋎ r

case mpr
F : Type u_1
inst✝⁴ : LogicalConnective F
inst✝³ : DecidableEq F
S : Type u_2
inst✝² : System F S
𝓢 : S
inst✝¹ : Minimal 𝓢
p q r : F
Γ Δ : List F
inst✝ : System.NegationEquiv 𝓢
⊢ 𝓢 ⊢! (p ⋎ q) ⋎ r → 𝓢 ⊢! p ⋎ q ⋎ r
case mpr
F : Type u_1
inst✝⁴ : LogicalConnective F
inst✝³ : DecidableEq F
S : Type u_2
inst✝² : System F S
𝓢 : S
inst✝¹ : Minimal 𝓢
p q r : F
Γ Δ : List F
inst✝ : System.NegationEquiv 𝓢
⊢ 𝓢 ⊢! (p ⋎ q) ⋎ r → 𝓢 ⊢! p ⋎ q ⋎ r