Theorem coss2 5164

Description: Subclass theorem for composition. (Contributed by NM, 5-Apr-2013.)

Assertion

Ref	Expression
coss2

Proof of Theorem coss2

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		id 22	. . . . . 6
2	1	ssbrd 4493	. . . . 5
3	2	anim1d 564	. . . 4
4	3	eximdv 1710	. . 3
5	4	ssopab2dv 4781	. 2
6		df-co 5013	. 2
7		df-co 5013	. 2
8	5, 6, 7	3sstr4g 3544	1

Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  C_wss 3475   class class class wbr 4452  {copab 4509  o.ccom 5008

This theorem is referenced by:  coeq2  5166  funss  5611  tposss  6975  dftpos4  6993  tsrdir  15868  mvdco  16470  ustex2sym  20719  ustex3sym  20720  ustund  20724  ustneism  20726  trust  20732  utop2nei  20753  neipcfilu  20799  fcoinver  27460  rtrclreclem.min  29070

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-in 3482  df-ss 3489  df-br 4453  df-opab 4511  df-co 5013