simp only [Formula.freeVarSet]
z : String
phi psi : Formula
phi_ih : ∀ (j : ℕ), (Formula.open j (free_ z) phi).freeVarSet ⊆ phi.freeVarSet ∪ {free_ z}
psi_ih : ∀ (j : ℕ), (Formula.open j (free_ z) psi).freeVarSet ⊆ psi.freeVarSet ∪ {free_ z}
j : ℕ
⊢ ((Formula.open j (free_ z) phi).imp_ (Formula.open j (free_ z) psi)).freeVarSet ⊆
    (phi.imp_ psi).freeVarSet ∪ {free_ z}
z : String
phi psi : Formula
phi_ih : ∀ (j : ℕ), (Formula.open j (free_ z) phi).freeVarSet ⊆ phi.freeVarSet ∪ {free_ z}
psi_ih : ∀ (j : ℕ), (Formula.open j (free_ z) psi).freeVarSet ⊆ psi.freeVarSet ∪ {free_ z}
j : ℕ
⊢ (Formula.open j (free_ z) phi).freeVarSet ∪ (Formula.open j (free_ z) psi).freeVarSet ⊆
    phi.freeVarSet ∪ psi.freeVarSet ∪ {free_ z}