The second syllogism takes the conditional established in the first and then denies its consequent.
First premise: If the claim is denied, an impossibility follows.
Second premise: But that impossibility does not hold.
Conclusion: Therefore the denial of the claim does not hold.
This applies the valid hypothetical rule denying the consequent entails denying the antecedent, studied earlier.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
The second syllogism takes the conditional established in the first and then denies its consequent.
First premise: If the claim is denied, an impossibility follows.
Second premise: But that impossibility does not hold.
Conclusion: Therefore the denial of the claim does not hold.
This applies the valid hypothetical rule denying the consequent entails denying the antecedent, studied earlier.