Derive the validity of universal form of part (a) of the elimination rule from the validity of universal instantiation and the valid argument called elimination in Section 2.3.

Step-by-step explanation:

Derive the validity of universal form of part (a) of the elimination rule from the validity of universal instantiation and the valid argument called elimination in Section 2.3.

P (x) ∨Q (x)

~Q (x)

∵ P (x)

Universal Instantiation has the following argument form

∀ x ∈ D, P (x)

P (a) for a particular a∈D

Universal Elimination Rule:

∀x, P (x)

∵~ P (a)

Here is a particular value.

P (a) For a particular a∈D

Since the universal elimination is same as universal instantiation.

Therefore, Universal elimination is valid when universal instantiation and elimination rule are valid