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Theorem rspcv 2625
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 1398 . 2 xψ
2 rspcv.1 . 2 (x = A → (φψ))
31, 2rspc 2623 1 (A B → (x B φψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1226   wcel 1370  wral 2280
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-v 2533
This theorem is referenced by:  rspccv  2626  rspcva  2627  rspccva  2628  rspc3v  2638  rr19.3v  2655  rr19.28v  2656  rspsbc  2813  intmin  3605  ralxfrALT  4145  funcnvuni  4890  acexmidlemcase  5427  grprinvlem  5614  grprinvd  5615  caofref  5651  tfrlem1  5841  tfrlem5  5848  tfrlem9  5853  rdgon  5889  prltlu  6335  prnmaxl  6336  prnminu  6337  bj-indsuc  7347  bj-inf2vnlem2  7385
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