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Theorem cbvcsb 3013
 Description: Change bound variables in a class substitution. Interestingly, this does not require any bound variable conditions on . (Contributed by Jeff Hankins, 13-Sep-2009.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
cbvcsb.1
cbvcsb.2
cbvcsb.3
Assertion
Ref Expression
cbvcsb

Proof of Theorem cbvcsb
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvcsb.1 . . . . 5
21nfcri 2276 . . . 4
3 cbvcsb.2 . . . . 5
43nfcri 2276 . . . 4
5 cbvcsb.3 . . . . 5
65eleq2d 2210 . . . 4
72, 4, 6cbvsbc 2942 . . 3
87abbii 2256 . 2
9 df-csb 3009 . 2
10 df-csb 3009 . 2
118, 9, 103eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   wcel 1481  cab 2126  wnfc 2269  wsbc 2914  csb 3008 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-sbc 2915  df-csb 3009 This theorem is referenced by:  cbvcsbv  3014  cbvsum  11181
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