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Theorem elrabsf 3201
 Description: Membership in a restricted class abstraction, expressed with explicit class substitution. (The variation elrabf 3093 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 3165 . 2
2 elrabsf.1 . . 3
3 nfcv 2574 . . 3
4 nfv 1630 . . 3
5 nfsbc1v 3182 . . 3
6 sbceq1a 3173 . . 3
72, 3, 4, 5, 6cbvrab 2956 . 2
81, 7elrab2 3096 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wcel 1726  wnfc 2561  crab 2711  wsbc 3163 This theorem is referenced by:  onminesb  4780  mpt2xopovel  6473  ac6num  8361  tfisg  25481  wfisg  25486  frinsg  25522  rabrenfdioph  26877  bnj23  29085  bnj1204  29383 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-sbc 3164
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