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Theorem csbabg 3029
 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 2954 . . . 4
2 df-clab 2102 . . . . 5
3 sbsbc 2884 . . . . 5
42, 3bitri 183 . . . 4
5 df-clab 2102 . . . . . 6
6 sbsbc 2884 . . . . . 6
75, 6bitri 183 . . . . 5
87sbcbii 2938 . . . 4
91, 4, 83bitr4i 211 . . 3
10 sbcel2g 2992 . . 3
119, 10syl5rbb 192 . 2
1211eqrdv 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1314   wcel 1463  wsb 1718  cab 2101  wsbc 2880  csb 2973 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-sbc 2881  df-csb 2974 This theorem is referenced by:  csbsng  3552  csbunig  3712  csbxpg  4588  csbdmg  4701  csbrng  4968
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