Description: Axiom of Specialization. A universally quantified wff implies the wff
without the universal quantifier (i.e., an instance, or special case, of
the generalized wff). In other words, if something is true for all
x , then it is true for any specific x (that would typically occur
as a free variable in the wff substituted for ph ). (A free variable
is one that does not occur in the scope of a quantifier: x and y
are both free in x = y , but only x is free in A. y x = y .)
Axiom scheme C5' in Megill p. 448 (p. 16 of the preprint). Also appears
as Axiom B5 of Tarski p. 67 (under his system S2, defined in the last
paragraph on p. 77).

Note that the converse of this axiom does not hold in general, but a
weaker inference form of the converse holds and is expressed as rule
ax-gen . Conditional forms of the converse are given by ax-13 ,
ax-c14 , ax-c16 , and ax-5 .

Unlike the more general textbook Axiom of Specialization, we cannot choose
a variable different from x for the special case. In our
axiomatization, that requires the assistance of equality axioms, and we
deal with it later after we introduce the definition of proper
substitution (see stdpc4 ).

This axiom is obsolete and should no longer be used. It is proved above
as Theorem sp . (Contributed by NM, 3-Jan-1993) Use sp instead.
(New usage is discouraged.)