unfold NoMetaVarAndAllFreeInList at h1
phi psi : Formula
phi_ih : ∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → phi.metaVarSet = ∅
psi_ih : ∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → psi.metaVarSet = ∅
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (phi.imp_ psi)
⊢ (phi.imp_ psi).metaVarSet = ∅
phi psi : Formula
phi_ih : ∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs phi → phi.metaVarSet = ∅
psi_ih : ∀ (vs : List VarName), NoMetaVarAndAllFreeInList vs psi → psi.metaVarSet = ∅
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi ∧ NoMetaVarAndAllFreeInList vs psi
⊢ (phi.imp_ psi).metaVarSet = ∅