Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbco Unicode version

Theorem csbco 3444
 Description: Composition law for chained substitutions into a class. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbco
Distinct variable group:   ,

Proof of Theorem csbco
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3435 . . . . . 6
21abeq2i 2584 . . . . 5
32sbcbii 3387 . . . 4
4 sbcco 3350 . . . 4
53, 4bitri 249 . . 3
65abbii 2591 . 2
7 df-csb 3435 . 2
8 df-csb 3435 . 2
96, 7, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434 This theorem is referenced by:  csbnest1g  3845  csbvarg  3848  fvmpt2curryd  7019  zsum  13540  fsum  13542  zprod  13744  fprod  13748  gsumply1eq  18347  sbccom2  30530  fsumsplitf  31568  dvmptmulf  31734  dvmptfprod  31742  bj-csbsn  34471 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328  df-csb 3435
 Copyright terms: Public domain W3C validator