| 0 | (A→B) ∧ (B→C) | assumption |
| 1 | A→B | simplification [0] |
| 2 | B→C | simplification [0] |
| 3 | A | assumption |
| 4 | B | modus ponens [3, 1] |
| 5 | C | modus ponens [4, 2] |
| 6 | A→C | conditional introduction [3, 5] |
| 7 | (A→B) ∧ (B→C)→(A→C) | conditional introduction [0, 6] |
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Hypothetical syllogism
Proof of the hypothetical syllogism (transitivity of the implication).
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