If something has the elements of design it is designed. (X is X, Law of identity)
Life has the elements of design
Therefore life is designed.
"If something is designed then it is designed" would be the law of identity.
To examine your proposition, which is different, we would have to know what you think "the elements of design" are.
We would then need to verify your premises by checking (a) whether all things which have these elements are indeed designed (b) whether life has those elements.
Now, suppose we cannot agree on whether things with what you denote as "the elements of design" really are always designed. Suppose I were to suggest that some of them, namely living organisms, were products of evolution. Then in order to establish the first premise, you would have to come up with some argument that living things are designed rather than evolved. Which is what you were trying to do in the first place: in order to make you argument for the design and against the evolution of organisms watertight, you would first have to construct a watertight argument for the design and against the evolution of organisms.