simp only [predVarSet] at h1
P : PredName
zs : List VarName
H : Formula
x : VarName
phi : Formula
phi_ih : phi.predVarSet = ∅ → replace P zs H phi = phi
h1 : (exists_ x phi).predVarSet = ∅
⊢ replace P zs H (exists_ x phi) = exists_ x phi
P : PredName
zs : List VarName
H : Formula
x : VarName
phi : Formula
phi_ih : phi.predVarSet = ∅ → replace P zs H phi = phi
h1 : phi.predVarSet = ∅
⊢ replace P zs H (exists_ x phi) = exists_ x phi