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Theorem csbie2g 3182
 Description: Conversion of implicit substitution to explicit class substitution. This version of sbcie 3080 avoids a disjointness condition on 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 3137 . 2
2 csbie2g.1 . . . . 5
32eleq2d 2420 . . . 4
4 csbie2g.2 . . . . 5
54eleq2d 2420 . . . 4
63, 5sbcie2g 3079 . . 3
76abbi1dv 2469 . 2
81, 7syl5eq 2397 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by: (None)
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