Prove the validity of the argument

p$$q$$r $(1)$

p$->$a$$s $(2)$

q$->$a$$s $(3)$

r$->$a$$s $(4)$

$$s $(5)$

$$a

Show all your steps. Label all the propositions inferred as they added to the premises, and mention all the rules of inference applied at each step with the premises involved. The rules of inference must be referred to by their names. There are rules of: addition, simplification, conjunction, modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, resolution.