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Theorem coss1 5163
Description: Subclass theorem for composition. (Contributed by FL, 30-Dec-2010.)
Assertion
Ref Expression
coss1

Proof of Theorem coss1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 22 . . . . . 6
21ssbrd 4493 . . . . 5
32anim2d 565 . . . 4
43eximdv 1710 . . 3
54ssopab2dv 4781 . 2
6 df-co 5013 . 2
7 df-co 5013 . 2
85, 6, 73sstr4g 3544 1
Colors of variables: wff setvar class
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:  coeq1  5165  funss  5611  tposss  6975  tsrdir  15868  ustex2sym  20719  ustex3sym  20720  ustund  20724  ustneism  20726  trust  20732  utop2nei  20753  neipcfilu  20799  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
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