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Theorem sbcie2g 3186
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3187 avoids a disjointness condition on by substituting twice. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
sbcie2g.1
sbcie2g.2
Assertion
Ref Expression
sbcie2g
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem sbcie2g
StepHypRef Expression
1 dfsbcq 3155 . 2
2 sbcie2g.2 . 2
3 sbsbc 3157 . . 3
4 nfv 1629 . . . 4
5 sbcie2g.1 . . . 4
64, 5sbie 2122 . . 3
73, 6bitr3i 243 . 2
81, 2, 7vtoclbg 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:  sbcel2gv  3213  csbie2g  3289  brab1  4249  riotasvd  6584  bnj90  29024  bnj124  29179 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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