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Theorem rspec 2420
Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)
Hypothesis
Ref Expression
rspec.1 𝑥𝐴 𝜑
Assertion
Ref Expression
rspec (𝑥𝐴𝜑)

Proof of Theorem rspec
StepHypRef Expression
1 rspec.1 . 2 𝑥𝐴 𝜑
2 rsp 2416 . 2 (∀𝑥𝐴 𝜑 → (𝑥𝐴𝜑))
31, 2ax-mp 7 1 (𝑥𝐴𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  wral 2353
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-ral 2358
This theorem is referenced by:  rspec2  2455  vtoclri  2682  isarep2  5037  ecopover  6291  ecopoverg  6294  indstr  8814
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