Theorem spi

Description: 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)

	Ref	Expression
Hypothesis	spi.1	$$⊢\forall x\phi$$
Assertion	spi	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		spi.1	$$⊢\forall x\phi$$
2		sp	$$⊢\forall x\phi \to \phi$$
3	1 2	ax-mp	$$⊢\phi$$