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Theorem csbco 3145
 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 3137 . . . . . 6
21abeq2i 2460 . . . . 5
32sbcbii 3101 . . . 4
4 sbcco 3068 . . . 4
53, 4bitri 240 . . 3
65abbii 2465 . 2
7 df-csb 3137 . 2
8 df-csb 3137 . 2
96, 7, 83eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wcel 1710  cab 2339  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbvarg  3163  csbnest1g  3188  eqerlem  5960
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