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Theorem csbie2g 2896
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 2797 avoids a disjointness condition on and by substituting twice. (Contributed by Mario Carneiro, 11-Nov-2016.)
Hypotheses
Ref Expression
csbie2g.1
csbie2g.2
Assertion
Ref Expression
csbie2g
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   (,)

Proof of Theorem csbie2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 2853 . 2
2 csbie2g.1 . . . . 5
32eleq2d 2107 . . . 4
4 csbie2g.2 . . . . 5
54eleq2d 2107 . . . 4
63, 5sbcie2g 2796 . . 3
76abbi1dv 2157 . 2
81, 7syl5eq 2084 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  cab 2026  wsbc 2764  csb 2852 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765  df-csb 2853 This theorem is referenced by: (None)
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