Original proofs; classical forall x: Calgary TFL package
NEGATION INTRODUCTION
Premises: P -> (Q and R), not Q. Goal: not P.
1 P -> (Q and R)  Premise
2 not Q           Premise
3 P               AS
4 Q and R         ->E 1,3
5 Q               and E 4
6 contradiction   not E 2,5
7 not P           not I 3-6
Block: 3-6.
INDIRECT PROOF
Premises: not P -> Q, not Q. Goal: P.
1 not P -> Q      Premise
2 not Q           Premise
3 not P           AS
4 Q               ->E 1,3
5 contradiction   not E 2,4
6 P               IP 3-5
Block: 3-5. Applying not I to that same block concludes not not P instead.
IP/DNE are classical rules in the stated package, not assumed available in every nonclassical system.