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.

Step	Hyp	Ref	Expression
1		df-clab 2443	. . . 4
2		sbsbc 3331	. . . 4
3	1, 2	bitri 249	. . 3
4		sbccom 3407	. . . 4
5		df-clab 2443	. . . . . 6
6		sbsbc 3331	. . . . . 6
7	5, 6	bitri 249	. . . . 5
8	7	sbcbii 3387	. . . 4
9	4, 8	bitr4i 252	. . 3
10		sbcel2 3831	. . 3
11	3, 9, 10	3bitrri 272	. 2
12	11	eqriv 2453	1

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