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Theorem cbvcsbw 3010
 Description: Version of cbvcsb 3011 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.)
Hypotheses
Ref Expression
cbvcsbw.1
cbvcsbw.2
cbvcsbw.3
Assertion
Ref Expression
cbvcsbw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem cbvcsbw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvcsbw.1 . . . . 5
21nfcri 2276 . . . 4
3 cbvcsbw.2 . . . . 5
43nfcri 2276 . . . 4
5 cbvcsbw.3 . . . . 5
65eleq2d 2210 . . . 4
72, 4, 6cbvsbcw 2939 . . 3
87abbii 2256 . 2
9 df-csb 3007 . 2
10 df-csb 3007 . 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 2912  csb 3006 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 2913  df-csb 3007 This theorem is referenced by:  cbvprod  11358
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