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Theorem rspec 2678
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 2674 . 2 (x A φ → (x Aφ))
31, 2ax-mp 5 1 (x Aφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wcel 1710  wral 2614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-ral 2619
This theorem is referenced by:  rspec2  2713  vtoclri  2929
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