In this paper we show how the assumption of the generalized continuum hypothesis (GCH) can be removed or partially removed from proofs in Zermelo-Frankel set theory (ZF) of statements expressible in the simple theory of types. We assume the reader is familiar with the latter language, especially with the classification of formulas and sentences of that language into Σκη and Πκη form (cf. [1]) and with how that language can be relatively interpreted into the language of ZF.