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Theorem sscrel 14738
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 14735 . 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 4977 1  |-  Rel  C_cat
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369   E.wex 1586    e. wcel 1756   E.wrex 2728   ~Pcpw 3872    X. cxp 4850   Rel wrel 4857    Fn wfn 5425   ` cfv 5430   X_cixp 7275    C_cat cssc 14732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4425  ax-nul 4433  ax-pr 4543
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-ne 2620  df-ral 2732  df-rex 2733  df-rab 2736  df-v 2986  df-dif 3343  df-un 3345  df-in 3347  df-ss 3354  df-nul 3650  df-if 3804  df-sn 3890  df-pr 3892  df-op 3896  df-opab 4363  df-xp 4858  df-rel 4859  df-ssc 14735
This theorem is referenced by:  brssc  14739  ssc1  14746  ssc2  14747  ssctr  14750  issubc  14760
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