Generation of a long process of a pyramidal cell, that carries efferent (outgoing) action potentials from the cell body in cerebral cortex layer V towards target cells in the gray matter of the spinal cord. This axonal process is a member of those that make up the corticospinal tract. [ GOC:cls GOC:dph http://www.ncbi.nlm.nih.gov/pubmed/9878731 GOC:dgh GOC:jid http://purl.obolibrary.org/obo/go/references/0000021 ]