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Theorem csbiebg 3175
 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 2362 . . . 4
21imbi1d 308 . . 3
32albidv 1625 . 2
4 csbeq1 3139 . . 3
54eqeq1d 2361 . 2
6 vex 2862 . . 3
7 csbiebg.2 . . 3
86, 7csbieb 3174 . 2
93, 5, 8vtoclbg 2915 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  wnfc 2476  csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 936  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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