Is this an argument by simplification: it can be done by doing Y, therefore it can be done?

Question

The problem is X This problem can be easily solved by doing Y

Therefore this problem can be easily solved

I am confused if this is Simplification (Which means the inference is Valid)

Answer 1

No. "Simplification" is typically use for the rule of conjunction elimination in propositional logic. This inference is not even propositional, it requires a predicate S(X,Y), "Y easily solves X", and goes like this S(X,Y) → ∃zS(X,z). This is valid, but not by conjunction elimination. It is called existential generalization.

In a way, it is similar in spirit: we are going from a more specific statement to a less specific one, as in simplification. Disjunction introduction and universal instantiation work that way too. Such inferences in logic are sometimes collectively called "weakening".