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Theorem fnfuc 14134
 Description: The FuncCat operation is a well-defined function on categories. (Contributed by Mario Carneiro, 12-Jan-2017.)
Assertion
Ref Expression
fnfuc FuncCat

Proof of Theorem fnfuc
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-fuc 14133 . 2 FuncCat Nat comp Nat Nat comp
2 tpex 4700 . 2 Nat comp Nat Nat comp
31, 2fnmpt2i 6412 1 FuncCat
 Colors of variables: wff set class Syntax hints:  csb 3243  ctp 3808  cop 3809   cmpt 4258   cxp 4868   wfn 5441  cfv 5446  (class class class)co 6073   cmpt2 6075  c1st 6339  c2nd 6340  cnx 13458  cbs 13461   chom 13532  compcco 13533  ccat 13881   cfunc 14043   Nat cnat 14130   FuncCat cfuc 14131 This theorem is referenced by:  fucbas  14149  fuchom  14150 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fv 5454  df-oprab 6077  df-mpt2 6078  df-1st 6341  df-2nd 6342  df-fuc 14133
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