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Theorem sbc6g 2938
 Description: An equivalence for class substitution. (Contributed by NM, 11-Oct-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Assertion
Ref Expression
sbc6g
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbc6g
StepHypRef Expression
1 sbc5 2937 . 2
2 nfe1 1473 . . 3
3 ceqex 2817 . . 3
42, 3ceqsalg 2718 . 2
51, 4bitr4id 198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1330   wceq 1332  wex 1469   wcel 1481  wsbc 2914 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-sbc 2915 This theorem is referenced by:  sbc6  2939  sbciegft  2944  ralsnsg  3569  ralsns  3570  fz1sbc  9927
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