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Theorem sbcie2g 3361
Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3362 avoids a disjointness condition on x,A by substituting twice. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
sbcie2g.1
sbcie2g.2
Assertion
Ref Expression
sbcie2g
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem sbcie2g
StepHypRef Expression
1 dfsbcq 3329 . 2
2 sbcie2g.2 . 2
3 sbsbc 3331 . . 3
4 nfv 1707 . . . 4
5 sbcie2g.1 . . . 4
64, 5sbie 2149 . . 3
73, 6bitr3i 251 . 2
81, 2, 7vtoclbg 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:  sbcel2gv  3394  csbie2g  3465  brab1  4497  bnj90  33775  bnj124  33929  riotasvd  34687
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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