Theorem spi

Inference rule of universal instantiation, or universal specialization. Converse of the inference rule of (universal) generalization [ax-gen]. Contrary to the rule of generalization, its closed form is valid, see sp. (Contributed by NM, 5-Aug-1993.)

Hypothesis
spi.1
\( \vdash \forall x \, \varphi \)
Conclusion
\( \vdash \varphi \)
Proof
l0
spi.1
\( \vdash \forall x \, \varphi \)
sp
\( \vdash \forall x \, \varphi \rightarrow \varphi \)
ax-mp l0 _