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Theorem spi 2173
Description: Inference rule of universal instantiation, or universal specialization. Converse of the inference rule of (universal) generalization ax-gen 1787. Contrary to the rule of generalization, its closed form is valid, see sp 2172. (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 2172 . 2 (∀𝑥𝜑𝜑)
31, 2ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-ex 1772
This theorem is referenced by:  dariiALT  2746  barbariALT  2750  festinoALT  2755  barocoALT  2757  daraptiALT  2765  kmlem2  9565  axac2  9876  axac  9877  axaci  9878  bnj864  32093  rr-grothprim  40513
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