The theorem to be proved here is a straightforward conditional: viz.

(AB)((BC)(AC)).(AB)((BC)(AC)).

No remaining use of an oracle can be present in a proof that constitutes a solution to this problem.

Goal: (implies (implies A B) (implies (implies B C) (implies A C)))

HyperSlate Bezier AthenCfromAthenBandBthenC [PROPOSITIONAL-CALCULUS): Saved with a symbols. PC Oracle) 1 (A= B) = (B= from 0 )= A= ) HyperSlate Bezier AthenCfromAthenBandBthenC [PROPOSITIONAL-CALCULUS): Saved with a symbols. PC Oracle) 1 (A= B) = (B= from 0 )= A= )