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Theorem dffun8 4872
Description: Alternate definition of a function. One possibility for the definition of a function in [Enderton] p. 42. Compare dffun7 4871. (Contributed by NM, 4-Nov-2002.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
dffun8  Fun  Rel  dom
Distinct variable group:   ,,

Proof of Theorem dffun8
StepHypRef Expression
1 dffun7 4871 . 2  Fun  Rel  dom
2 df-mo 1901 . . . . 5
3 vex 2554 . . . . . . 7 
_V
43eldm 4475 . . . . . 6  dom
5 pm5.5 231 . . . . . 6
64, 5sylbi 114 . . . . 5  dom
72, 6syl5bb 181 . . . 4  dom
87ralbiia 2332 . . 3  dom  dom
98anbi2i 430 . 2  Rel  dom  Rel  dom
101, 9bitri 173 1  Fun  Rel  dom
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wex 1378   wcel 1390  weu 1897  wmo 1898  wral 2300   class class class wbr 3755   dom cdm 4288   Rel wrel 4293   Fun wfun 4839
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-id 4021  df-cnv 4296  df-co 4297  df-dm 4298  df-fun 4847
This theorem is referenced by:  funco  4883  funimaexglem  4925  funfveu  5131
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