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Metamath Proof Explorer

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	$⊢ \forall x φ$
	Assertion	spi	$⊢ φ$

Proof

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