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Theorem cbvcsb 3247
 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 2565 . . . 4
3 cbvcsb.2 . . . . 5
43nfcri 2565 . . . 4
5 cbvcsb.3 . . . . 5
65eleq2d 2502 . . . 4
72, 4, 6cbvsbc 3181 . . 3
87abbii 2547 . 2
9 df-csb 3244 . 2
10 df-csb 3244 . 2
118, 9, 103eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2421  wnfc 2558  wsbc 3153  csb 3243 This theorem is referenced by:  cbvcsbv  3248  cbvsum  12481  measiuns  24563  cbvprod  25233 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-sbc 3154  df-csb 3244
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