An instance of L3 is
(1)
Using the first assumed logical derivation and modus ponens rule gives . The L2 instance for these same three propositional formulas is
(2)
Use the other assumed logical derivation and then the newly obtained logical derivation in two applications of modus ponens rule. Therefore
(3)
This conditional modus ponens construction is the step needed to discharge assumptions from a modus ponens rule line in part (iv).

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