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Theorem coss12d 37462
 Description: Subset deduction for composition of two classes. (Contributed by Richard Penner, 24-Dec-2019.)
Hypotheses
Ref Expression
coss12d.a
coss12d.c
Assertion
Ref Expression
coss12d

Proof of Theorem coss12d
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 coss12d.c . . . . . 6
21ssbrd 4478 . . . . 5
3 coss12d.a . . . . . 6
43ssbrd 4478 . . . . 5
52, 4anim12d 563 . . . 4
65eximdv 1697 . . 3
76ssopab2dv 4766 . 2
8 df-co 4998 . 2
9 df-co 4998 . 2
107, 8, 93sstr4g 3530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369  wex 1599   wss 3461   class class class wbr 4437  copab 4494   ccom 4993 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-in 3468  df-ss 3475  df-br 4438  df-opab 4496  df-co 4998 This theorem is referenced by:  trrelssd  37470
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