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Theorem csbiebg 3290
 Description: Bidirectional conversion between an implicit class substitution hypothesis and its explicit substitution equivalent. (Contributed by NM, 24-Mar-2013.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
csbiebg.2
Assertion
Ref Expression
csbiebg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem csbiebg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2445 . . . 4
21imbi1d 309 . . 3
32albidv 1635 . 2
4 csbeq1 3254 . . 3
54eqeq1d 2444 . 2
6 vex 2959 . . 3
7 csbiebg.2 . . 3
86, 7csbieb 3289 . 2
93, 5, 8vtoclbg 3012 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  wnfc 2559  csb 3251 This theorem is referenced by:  cdlemefrs29bpre0  31193 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-csb 3252
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