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

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