Use the two derived inference rules whose complete proofs were supplied in (d). The following logical derivation has no nested hypothetical subproofs:
1  P → Q                           premise
2  Q → R                           premise
3  P → (Q → R)                     → creation from 2
4  (P → Q) → (P → R)               → distribution from 3
5  P → R                           →-elim, 1 and 4
The creation instance takes and . The distribution instance takes . The metarules are justified in (d); this requested flat use does not secretly invoke implication introduction rule in one of its own lines.

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