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Theorem sbc8g 3168
 Description: This is the closest we can get to df-sbc 3162 if we start from dfsbcq 3163 (see its comments) and dfsbcq2 3164. (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 3163 . 2
2 eleq1 2496 . 2
3 df-clab 2423 . . 3
4 equid 1688 . . . 4
5 dfsbcq2 3164 . . . 4
64, 5ax-mp 8 . . 3
73, 6bitr2i 242 . 2
81, 2, 7vtoclbg 3012 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wsb 1658   wcel 1725  cab 2422  wsbc 3161 This theorem is referenced by:  rusbcALT  27616  bnj984  29323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162
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