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Theorem sbcbig 3199
 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 3156 . 2
2 dfsbcq2 3156 . . 3
3 dfsbcq2 3156 . . 3
42, 3bibi12d 313 . 2
5 sbbi 2145 . 2
61, 4, 5vtoclbg 3004 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652  wsb 1658   wcel 1725  wsbc 3153 This theorem is referenced by:  sbcabel  3230  sbcbi  28561  sbc3orgVD  28900  sbcbiVD  28925  bnj89  29023 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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