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Theorem rspec 2347
Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)
Hypothesis
Ref Expression
rspec.1 x A φ
Assertion
Ref Expression
rspec (x Aφ)

Proof of Theorem rspec
StepHypRef Expression
1 rspec.1 . 2 x A φ
2 rsp 2343 . 2 (x A φ → (x Aφ))
31, 2ax-mp 7 1 (x Aφ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1370  wral 2280
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1377
This theorem depends on definitions:  df-bi 110  df-ral 2285
This theorem is referenced by:  rspec2  2382  vtoclri  2601  isarep2  4908  ecopover  6111  ecopoverg  6114
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