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Theorem sscrel 13706
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 13703 . 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 4827 1  |-  Rel  C_cat
Colors of variables: wff set class
Syntax hints:    /\ wa 358   E.wex 1531    e. wcel 1696   E.wrex 2557   ~Pcpw 3638    X. cxp 4703   Rel wrel 4710    Fn wfn 5266   ` cfv 5271   X_cixp 6833    C_cat cssc 13700
This theorem is referenced by:  brssc  13707  ssc1  13714  ssc2  13715  ssctr  13718  issubc  13728
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-opab 4094  df-xp 4711  df-rel 4712  df-ssc 13703
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