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Theorem sbcie2g 3289
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3290 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 3257 . 2
2 sbcie2g.2 . 2
3 sbsbc 3259 . . 3
4 nfv 1769 . . . 4
5 sbcie2g.1 . . . 4
64, 5sbie 2257 . . 3
73, 6bitr3i 259 . 2
81, 2, 7vtoclbg 3094 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wceq 1452  wsb 1805   wcel 1904  wsbc 3255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033  df-sbc 3256 This theorem is referenced by:  sbcel2gv  3315  csbie2g  3380  brab1  4441  bnj90  29600  bnj124  29754  riotasvd  32592
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