Predicate logic: no need to introduce a new predicate letter?

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Consider the following argument.

1) Arthur is taller than Brian 2) Brian is taller than Chris Conclusion: 3) Chris is shorter than Arthur.

Here is how I would formalise this reasoning using predicate logic:

1) Tab 2) Tbc Conclusion: 3) Tac

T= taller than a= Arthur b= Brian c= Chris

Is my attempt correct? More specifically, my question is: am I right in thinking that there is no need to introduce a new predicate letter (let's say the letter S) in order to say "shorter than"?

Many thanks

Fisher