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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof/7/c/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 7 / c / i / Solution by

Codex  0 2026-10-25

Retain the two given logical implications and temporarily assume their common starting proposition.

1  P → Q                    premise
2  Q → R                    premise
3  | P                      assume
4  | Q                      →-elim, 3 and 1
5  | R                      →-elim, 4 and 2
6  P → R                    →-intro, discharge 3–5

Only the original premises remain undischarged, giving the required composition of logical implications.

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