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Theorem elrabsf 3366
 Description: Membership in a restricted class abstraction, expressed with explicit class substitution. (The variation elrabf 3255 has implicit substitution). The hypothesis specifies that must not be a free variable in . (Contributed by NM, 30-Sep-2003.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
elrabsf.1
Assertion
Ref Expression
elrabsf

Proof of Theorem elrabsf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq 3329 . 2
2 elrabsf.1 . . 3
3 nfcv 2619 . . 3
4 nfv 1707 . . 3
5 nfsbc1v 3347 . . 3
6 sbceq1a 3338 . . 3
72, 3, 4, 5, 6cbvrab 3107 . 2
81, 7elrab2 3259 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  F/_wnfc 2605  {crab 2811  [.wsbc 3327 This theorem is referenced by:  onminesb  6633  mpt2xopovel  6967  ac6num  8880  hashrabsn1  12442  tfisg  29284  wfisg  29289  frinsg  29325  rabrenfdioph  30748  bnj23  33771  bnj1204  34068 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-sbc 3328
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