simp only [def_iff_]
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)))
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
    ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P)))))