apply IsDeduct.mp_ P.not_
case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) S.not_
case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ S.not_)

case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_