apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q))))
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
    (((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))).imp_
      (((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))))

case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))