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Theorem rspec 3232
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 3229 . 2 (∀𝑥𝐴 𝜑 → (𝑥𝐴𝜑))
31, 2ax-mp 5 1 (𝑥𝐴𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  wral 3061
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-ex 1783  df-ral 3062
This theorem is referenced by:  rspec2  3261  vtoclri  3544  wfis  6310  wfis2f  6313  wfis2  6315  isarep2  6593  mpoexw  8012  ecopover  8763  frins  9693  alephsuc2  10021  indstr  12846  reltxrnmnf  13267  ackbijnn  15718  mrelatglb0  18455  0frgp  19566  iccpnfcnv  24323  prter2  37389  natlocalincr  45201  natglobalincr  45202
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