I'm not familiar with phrasing arguments in the form of traditional logical syllogisms, so I'd like to ask if this formulation is correct, or if it can be expressed more concisely. Note, I'm not asking for an evaluation of the argument itself.
P: If a life-form is not useful, it is inferior
P: Non-human animals are not useful
C: Therefore, non-human animals are inferior
P: If an animal is inferior, it can be exploited
P: Non-human animals are inferior
C: Therefore, non-human animals can be exploited