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Theorem rspcv 2951
Description: Restricted specialization, using implicit substitution. (Contributed by NM, 26-May-1998.)
Hypothesis
Ref Expression
rspcv.1 (x = A → (φψ))
Assertion
Ref Expression
rspcv (A B → (x B φψ))
Distinct variable groups:   x,A   x,B   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem rspcv
StepHypRef Expression
1 nfv 1619 . 2 xψ
2 rspcv.1 . 2 (x = A → (φψ))
31, 2rspc 2949 1 (A B → (x B φψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   = wceq 1642   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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861
This theorem is referenced by:  rspccv  2952  rspcva  2953  rspccva  2954  rspc3v  2964  rr19.3v  2980  rr19.28v  2981  rspsbc  3124  intmin  3946  evenodddisj  4516  nnadjoin  4520  tfinnn  4534  spfinsfincl  4539  funcnvuni  5161  nnc3n3p1  6278  nchoicelem12  6300  nchoicelem19  6307
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