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Theorem csbab 3855
Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Revised by NM, 19-Aug-2018.)
Assertion
Ref Expression
csbab
Distinct variable groups:   ,   ,

Proof of Theorem csbab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clab 2443 . . . 4
2 sbsbc 3331 . . . 4
31, 2bitri 249 . . 3
4 sbccom 3407 . . . 4
5 df-clab 2443 . . . . . 6
6 sbsbc 3331 . . . . . 6
75, 6bitri 249 . . . . 5
87sbcbii 3387 . . . 4
94, 8bitr4i 252 . . 3
10 sbcel2 3831 . . 3
113, 9, 103bitrri 272 . 2
1211eqriv 2453 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434
This theorem is referenced by:  csbsng  4088  csbuni  4277  csbxp  5086  csbdm  5202  csbwrdg  12570  abfmpeld  27492  abfmpel  27493
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-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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