apply rule_C P (exists_ v Q) v {exists_ v P, forall_ v (P.iff_ Q)}
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v Q)
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v P)

case h1.h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (exists_ v Q)

case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v P, forall_ v (P.iff_ Q)}, ¬isFreeIn v H

case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (exists_ v Q)