No variable is (effectively) free in a theorem.

This and later "hypothesis-building" lemmas, with labels starting "hb...", allow to construct proofs of formulas of the form \( \vdash \varphi \rightarrow \forall x \, \varphi \) from smaller formulas of this form. These are useful for constructing hypotheses that state " \( x \) is (effectively) not free in \( \varphi \) ". (Contributed by NM, 11-May-1993.) This hb* idiom is generally being replaced by the nf* idiom (see nfth ), but keeps its interest in some cases. (Revised by BJ, 23-Sep-2022.)