25f Use the objective case for subjects and objects of infinitives.

An infinitive is the word to followed by the base form of a verb. (See 42b.) Both subjects and objects of infinitives take the objective case.

The example reads,

Sue asked John and (strikethrough) I (end strikethrough) (insert) me (end insert) to drive the mayor and (strikethrough) she (end strikethrough) (insert) her (end insert) to the airport.

Text below reads, (Italics) John and me (End Italics) is the subject of the infinitive (Italics) to drive; mayor and her (End Italics) is the direct object of the infinitive.