To chain two conditionals, the consequent of the first must properly connect with the antecedent of the second:
1. If A, then B.
2. If B, then C.
Therefore: If A, then C.
In a reductio, the starting condition is the contradictory of the claim and the end is an impossibility. Intermediate steps may vary, but each entailment must be established.
Unrelated consequents and antecedents cannot be linked to obtain the desired conclusion.