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Theorem rspec 2416
Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)
Hypothesis
Ref Expression
rspec.1  |-  A. x  e.  A  ph
Assertion
Ref Expression
rspec  |-  ( x  e.  A  ->  ph )

Proof of Theorem rspec
StepHypRef Expression
1 rspec.1 . 2  |-  A. x  e.  A  ph
2 rsp 2412 . 2  |-  ( A. x  e.  A  ph  ->  ( x  e.  A  ->  ph ) )
31, 2ax-mp 7 1  |-  ( x  e.  A  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   A.wral 2349
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 2354
This theorem is referenced by:  rspec2  2451  vtoclri  2674  isarep2  5017  ecopover  6270  ecopoverg  6273  indstr  8762
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