Description: Proper substitution of a class for a set in a wff given equal classes.
This is the essence of the sixth axiom of Frege, specifically Proposition
52 of Frege1879 p. 50.

This theorem, which is similar to Theorem 6.7 of Quine p. 42 and holds
under both our definition and Quine's, provides us with a weak definition
of the proper substitution of a class for a set. Since our df-sbc does
not result in the same behavior as Quine's for proper classes, if we
wished to avoid conflict with Quine's definition we could start with this
theorem and dfsbcq2 instead of df-sbc . ( dfsbcq2 is needed because
unlike Quine we do not overload the df-sb syntax.) As a consequence of
these theorems, we can derive sbc8g , which is a weaker version of
df-sbc that leaves substitution undefined when A is a proper class.

However, it is often a nuisance to have to prove the sethood hypothesis of
sbc8g , so we will allow direct use of df-sbc after theorem sbc2or below. Proper substitution with a proper class is rarely needed, and when
it is, we can simply use the expansion of Quine's definition.
(Contributed by NM, 14-Apr-1995)