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Theorem sbcralg 3351
 Description: Interchange class substitution and restricted quantifier. (Contributed by NM, 15-Nov-2005.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
sbcralg
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   (,)

Proof of Theorem sbcralg
StepHypRef Expression
1 nfcv 2564 . 2
2 sbcralt 3349 . 2
31, 2mpan2 669 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wcel 1842  wnfc 2550  wral 2753  wsbc 3276 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-v 3060  df-sbc 3277 This theorem is referenced by:  r19.12sn  4036  r19.12snOLD  4037  bnj538  29110  cdlemkid3N  33932  cdlemkid4  33933  rspsbc2  36305  rspsbc2VD  36665
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