Theorem csbopabgALT 4785

Description: Move substitution into a class abstraction. Version of csbopab 4784 with a sethood antecedent but depending on fewer axioms. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
csbopabgALT

Distinct variable groups:   ,,   ,,

Proof of Theorem csbopabgALT

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		csbeq1 3437	. . 3
2		dfsbcq2 3330	. . . 4
3	2	opabbidv 4515	. . 3
4	1, 3	eqeq12d 2479	. 2
5		vex 3112	. . 3
6		nfs1v 2181	. . . 4
7	6	nfopab 4517	. . 3
8		sbequ12 1992	. . . 4
9	8	opabbidv 4515	. . 3
10	5, 7, 9	csbief 3459	. 2
11	4, 10	vtoclg 3167	1

Syntax hints:  ->wi 4  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327  [_csb 3434  {copab 4509

This theorem is referenced by:  csbcnvgALT  5192

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-an 371  df-3an 975  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  df-opab 4511