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Theorem csbabg 3197
 Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
csbabg
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem csbabg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbccom 3117 . . . 4
2 df-clab 2340 . . . . 5
3 sbsbc 3050 . . . . 5
42, 3bitri 240 . . . 4
5 df-clab 2340 . . . . . 6
6 sbsbc 3050 . . . . . 6
75, 6bitri 240 . . . . 5
87sbcbii 3101 . . . 4
91, 4, 83bitr4i 268 . . 3
10 sbcel2g 3157 . . 3
119, 10syl5rbb 249 . 2
1211eqrdv 2351 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642  wsb 1648   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:  csbsng  3785  csbunig  3899  csbxpg  4813  csbrng  4966
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