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Hypothetical syllogism

Proof of the hypothetical syllogism (transitivity of the implication).
0(A→B) ∧ (B→C)assumption
1A→Bsimplification [0]
2B→Csimplification [0]
3Aassumption
4Bmodus ponens [3, 1]
5Cmodus ponens [4, 2]
6A→Cconditional introduction [3, 5]
7(A→B) ∧ (B→C)→(A→C)conditional introduction [0, 6]
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