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Theorem sbc3angOLD 3391
Description: Distribution of class substitution over triple conjunction. (Contributed by NM, 14-Dec-2006.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) Obsolete as of 17-Aug-2018. Use sbc3an 3390 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbc3angOLD

Proof of Theorem sbc3angOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3330 . 2
2 dfsbcq2 3330 . . 3
3 dfsbcq2 3330 . . 3
4 dfsbcq2 3330 . . 3
52, 3, 43anbi123d 1299 . 2
6 sb3an 2141 . 2
71, 5, 6vtoclbg 3168 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327
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-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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