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Theorem spi 2185
Description: Inference rule of universal instantiation, or universal specialization. Converse of the inference rule of (universal) generalization ax-gen 1797. Contrary to the rule of generalization, its closed form is valid, see sp 2184. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spi.1 𝑥𝜑
Assertion
Ref Expression
spi 𝜑

Proof of Theorem spi
StepHypRef Expression
1 spi.1 . 2 𝑥𝜑
2 sp 2184 . 2 (∀𝑥𝜑𝜑)
31, 2ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  dariiALT  2754  barbariALT  2758  festinoALT  2763  barocoALT  2765  daraptiALT  2773  nfnfc  2994  kmlem2  9575  axac2  9886  axac  9887  axaci  9888  bnj864  32251  rr-grothprim  40928
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