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Theorem csbco 3262
 Description: Composition law for chained substitutions into a class. (Contributed by NM, 10-Nov-2005.)
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 3254 . . . . . 6
21abeq2i 2545 . . . . 5
32sbcbii 3218 . . . 4
4 sbcco 3185 . . . 4
53, 4bitri 242 . . 3
65abbii 2550 . 2
7 df-csb 3254 . 2
8 df-csb 3254 . 2
96, 7, 83eqtr4i 2468 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cab 2424  wsbc 3163  csb 3253 This theorem is referenced by:  csbvarg  3280  csbnest1g  3305  zsum  12514  fsum  12516  zprod  25265  fprod  25269 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-csb 3254
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