Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  csbco Unicode version

Theorem csbco 2889
 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 2881 . . . . . 6
21abeq2i 2164 . . . . 5
32sbcbii 2845 . . . 4
4 sbcco 2808 . . . 4
53, 4bitri 177 . . 3
65abbii 2169 . 2
7 df-csb 2881 . 2
8 df-csb 2881 . 2
96, 7, 83eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wceq 1259   wcel 1409  cab 2042  wsbc 2787  csb 2880 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-sbc 2788  df-csb 2881 This theorem is referenced by:  csbvarg  2905  csbnest1g  2929
 Copyright terms: Public domain W3C validator