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

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