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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	⊢ ∀ 𝑥 𝜑
	Assertion	spi	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		spi.1	⊢ ∀ 𝑥 𝜑
2		sp	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )
3	1 2	ax-mp	⊢ 𝜑