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

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