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Theorem sbc8g 2765
 Description: This is the closest we can get to df-sbc 2759 if we start from dfsbcq 2760 (see its comments) and dfsbcq2 2761. (Contributed by NM, 18-Nov-2008.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbc8g

Proof of Theorem sbc8g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq 2760 . 2
2 eleq1 2097 . 2
3 df-clab 2024 . . 3
4 equid 1586 . . . 4
5 dfsbcq2 2761 . . . 4
64, 5ax-mp 7 . . 3
73, 6bitr2i 174 . 2
81, 2, 7vtoclbg 2608 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wcel 1390  wsb 1642  cab 2023  wsbc 2758 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759 This theorem is referenced by:  bj-elssuniab  9245
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