Theorem csbiotagOLD 5586

Description: Class substitution within a description binder. (Contributed by Scott Fenton, 6-Oct-2017.) Obsolete as of 23-Aug-2018. Use csbiota 5585 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
csbiotagOLD

Distinct variable groups:   ,   ,

Proof of Theorem csbiotagOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		csbeq1 3437	. . 3
2		dfsbcq2 3330	. . . 4
3	2	iotabidv 5577	. . 3
4	1, 3	eqeq12d 2479	. 2
5		vex 3112	. . 3
6		nfs1v 2181	. . . 4
7	6	nfiota 5560	. . 3
8		sbequ12 1992	. . . 4
9	8	iotabidv 5577	. . 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  iotacio 5554

This theorem is referenced by:  csbfv12gOLD  5907

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-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-csb 3435  df-sn 4030  df-uni 4250  df-iota 5556