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Theorem csbco 3019
 Description: Composition law for chained substitutions into a class. Use the weaker csbcow 3020 when possible. (Contributed by NM, 10-Nov-2005.) (New usage is discouraged.)
Assertion
Ref Expression
csbco
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem csbco
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3010 . . . . . 6
21abeq2i 2252 . . . . 5
32sbcbii 2974 . . . 4
4 sbcco 2936 . . . 4
53, 4bitri 183 . . 3
65abbii 2257 . 2
7 df-csb 3010 . 2
8 df-csb 3010 . 2
96, 7, 83eqtr4i 2172 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   wcel 2112  cab 2127  wsbc 2915  csb 3009 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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-sbc 2916  df-csb 3010 This theorem is referenced by:  csbcow  3020  csbvarg  3037  csbnest1g  3062  zsumdc  11214  fsum3  11217  fsumsplitf  11238
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