In a paper that was written some time ago but appeared only recently [1], I indicated that Quine's system of quantification in [2], as well as his inclusive system of [3] can be modified so as to make it possible to prove *119 of [2] by another method than the one discovered by Berry. The reason originally given in [1, p. 136] for preferring the modified systems was wrong. (See [1, p. 158] for correction of previous remark.) But, at the cost of a slight complication of one of the axiom schemata, a considerable simplification of the proof of *119 is achieved in the modified systems, by dispensing with the use of *115 and *117 as intermediaries.