Page:CarmichealPostulates.djvu/24

This page has been validated.

Theorem XII. Postulates (MB) and formulae (A) are a logical equivalent of postulates (MVLR).

An analysis of the proof of formulae (A) will show that they follow directly from theorems IV., VI., VII. and postulate V. Hence we have the following theorem as a corollary of the preceding:

Theorem XIII. Postulates (MVB) and theorems IV., VI., VII. are a logical equivalent of postulates (MVLR).

Indiana University,
June, 1912.