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Theorem sscrel 14015
Description: The subcategory subset relation is a relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Assertion
Ref Expression
sscrel  |-  Rel  C_cat

Proof of Theorem sscrel
Dummy variables  h  j  s  t  x are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ssc 14012 . 2  |-  C_cat  =  { <. h ,  j >.  |  E. t ( j  Fn  ( t  X.  t )  /\  E. s  e.  ~P  t
h  e.  X_ x  e.  ( s  X.  s
) ~P ( j `
 x ) ) }
21relopabi 5002 1  |-  Rel  C_cat
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1551    e. wcel 1726   E.wrex 2708   ~Pcpw 3801    X. cxp 4878   Rel wrel 4885    Fn wfn 5451   ` cfv 5456   X_cixp 7065    C_cat cssc 14009
This theorem is referenced by:  brssc  14016  ssc1  14023  ssc2  14024  ssctr  14027  issubc  14037
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269  df-xp 4886  df-rel 4887  df-ssc 14012
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