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Theorem rspcv 2646
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 1418 . 2 xψ
2 rspcv.1 . 2 (x = A → (φψ))
31, 2rspc 2644 1 (A B → (x B φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553
This theorem is referenced by:  rspccv  2647  rspcva  2648  rspccva  2649  rspc3v  2659  rr19.3v  2676  rr19.28v  2677  rspsbc  2834  intmin  3626  ralxfrALT  4165  funcnvuni  4911  acexmidlemcase  5450  grprinvlem  5637  grprinvd  5638  caofref  5674  tfrlem1  5864  tfrlem5  5871  tfrlem9  5876  rdgon  5913  prltlu  6470  prnmaxl  6471  prnminu  6472  cauappcvgprlemm  6617  cauappcvgprlemladdru  6628  cauappcvgprlemladdrl  6629  caucvgprlemm  6639  nnsub  7733  ublbneg  8324  fzrevral  8737  iseqovex  8899  iseqval  8900  iseqfn  8901  iseq1  8902  iseqcl  8903  iseqp1  8904  iseqfveq2  8905  iseqfveq  8907  bj-indsuc  9387  bj-inf2vnlem2  9431
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