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Say I have

a > c && c > b

What function can eliminate c to yield:

a > b

A lot like:

Eliminate[a == c && c == b, c]

but for inequalities

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    $\begingroup$ I suspect Resolve is the function of choice for this. In[92]:= Resolve[Exists[c, a > c && c > b], {a, b}, Reals] Out[92]= b < a $\endgroup$ Sep 21 '16 at 18:34
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This is fairly close:

Reduce[a > c && c > b, {a, b}, {c}]
(*  a ∈ Reals && b < a  *)

Reference for this (now undocumented) form of the third argument of Solve/Reduce: Behavior of Reduce with variables as domain

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  • $\begingroup$ I didn't know you can pass that as domain... $\endgroup$
    – kozner
    Sep 20 '16 at 23:56
  • $\begingroup$ @kozner If you read Mr.Wizard's answer to the linked question, you'll see that this form for the "domain" is interpreted as a list of variables to be eliminated. It used to be documented, but the form was dropped from the documentation a few versions ago. $\endgroup$
    – Michael E2
    Sep 21 '16 at 0:03

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