apply IsDeduct.mp_ (P.imp_ ((P.imp_ P).imp_ P))
case a
P : Formula
⊢ IsDeduct ∅ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P))
case a.a
P : Formula
⊢ IsDeduct ∅ ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)))

case a.a
P : Formula
⊢ IsDeduct ∅ (P.imp_ ((P.imp_ P).imp_ P))