An axiom scheme of standard predicate calculus that emulates Axiom 5 of [Mendelson] p. 69. The hypothesis \( \Finv x \, \varphi \) can be thought of as emulating " \( x \) is not free in \( \varphi \) ". With this definition, the meaning of "not free" is less restrictive than the usual textbook definition; for example \( x \) would not (for us) be free in \( x = x \) by nfequid. This theorem scheme can be proved as a metatheorem of Mendelson's axiom system, even though it is slightly stronger than his Axiom 5. See stdpc5v for a version requiring fewer axioms. (Contributed by NM, 22-Sep-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) Remove dependency on [ax-10]. (Revised by Wolf Lammen, 4-Jul-2021.) (Proof shortened by Wolf Lammen, 11-Oct-2021.)