cases h1
P_u P_v : Formula
u v : VarName
h1 :
  ¬isFreeIn v P_u ∧
    ¬isFreeIn u P_v ∧
      fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v))
case intro
P_u P_v : Formula
u v : VarName
left✝ : ¬isFreeIn v P_u
right✝ :
  ¬isFreeIn u P_v ∧
    fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v))