Three terms (major, middle and minor) must be involved. [fact]
Three terms (major, middle and minor) must be involved in every valid syllogism. Any categorical syllogism that contains more than three terms is said to commit the formal Fallacy of Four Terms (quaternio terminorem) (see Chapter 10).
Ruggero J. Aldisert, Agatha D. Aldisert, Logic for Lawyers- A Guide …, loc. 455