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Theorem sscrel 15718
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 15715 . 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 4959 1  |-  Rel  C_cat
Colors of variables: wff setvar class
Syntax hints:    /\ wa 371   E.wex 1663    e. wcel 1887   E.wrex 2738   ~Pcpw 3951    X. cxp 4832   Rel wrel 4839    Fn wfn 5577   ` cfv 5582   X_cixp 7522    C_cat cssc 15712
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-opab 4462  df-xp 4840  df-rel 4841  df-ssc 15715
This theorem is referenced by:  brssc  15719  ssc1  15726  ssc2  15727  ssctr  15730  issubc  15740
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