apply proof_imp_deduct
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))