Theorem csbabgOLD 3856

Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) Obsolete as of 19-Aug-2018. Use csbab 3855 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
csbabgOLD

Distinct variable groups:   ,   ,

Proof of Theorem csbabgOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sbccom 3407	. . . 4
2		df-clab 2443	. . . . 5
3		sbsbc 3331	. . . . 5
4	2, 3	bitri 249	. . . 4
5		df-clab 2443	. . . . . 6
6		sbsbc 3331	. . . . . 6
7	5, 6	bitri 249	. . . . 5
8	7	sbcbii 3387	. . . 4
9	1, 4, 8	3bitr4i 277	. . 3
10		sbcel2gOLD 3832	. . 3
11	9, 10	syl5rbb 258	. 2
12	11	eqrdv 2454	1

Syntax hints:  ->wi 4  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434

This theorem is referenced by:  csbunigOLD  4278  csbxpgOLD  5087  csbrngOLD  5474  csbfv12gALTOLD  33621  csbingVD  33684  csbsngVD  33693  csbxpgVD  33694  csbrngVD  33696  csbunigVD  33698  csbfv12gALTVD  33699

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-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