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Theorem sbcbig 3374
 Description: Distribution of class substitution over biconditional. (Contributed by Raph Levien, 10-Apr-2004.)
Assertion
Ref Expression
sbcbig

Proof of Theorem sbcbig
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3330 . 2
2 dfsbcq2 3330 . . 3
3 dfsbcq2 3330 . . 3
42, 3bibi12d 321 . 2
5 sbbi 2142 . 2
61, 4, 5vtoclbg 3168 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327 This theorem is referenced by:  sbcbi1  3377  sbcabel  3416  sbcbi  33310  sbc3orgVD  33651  sbcbiVD  33676  bnj89  33774  bj-sbeq  34468  bj-sbceqgALT  34469 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-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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