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Theorem strcat 25760
 Description: Structure of a category. (Contributed by FL, 26-Oct-2007.)
Assertion
Ref Expression
strcat

Proof of Theorem strcat
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-catOLD 25753 . 2
2 stcat 25044 . 2
31, 2eqsstri 3208 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wex 1528   wceq 1623   wcel 1684  cab 2269  wral 2543  cvv 2788   wss 3152  cop 3643   cxp 4687   cdm 4689  cfv 5255  (class class class)co 5858  cded 25734   ccatOLD 25752 This theorem is referenced by:  relcat  25761  reldcat  25762  relrcat  25763  issubcata  25846 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-catOLD 25753
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