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Theorem dffun9 4873
Description: Alternate definition of a function. (Contributed by NM, 28-Mar-2007.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
dffun9  Fun  Rel  dom  ran
Distinct variable group:   ,,

Proof of Theorem dffun9
StepHypRef Expression
1 dffun7 4871 . 2  Fun  Rel  dom
2 vex 2554 . . . . . . . 8 
_V
3 vex 2554 . . . . . . . 8 
_V
42, 3brelrn 4510 . . . . . . 7  ran
54pm4.71ri 372 . . . . . 6  ran
65mobii 1934 . . . . 5  ran
7 df-rmo 2308 . . . . 5  ran  ran
86, 7bitr4i 176 . . . 4  ran
98ralbii 2324 . . 3  dom  dom  ran
109anbi2i 430 . 2  Rel  dom  Rel  dom  ran
111, 10bitri 173 1  Fun  Rel  dom  ran
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wcel 1390  wmo 1898  wral 2300  wrmo 2303   class class class wbr 3755   dom cdm 4288   ran crn 4289   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-rmo 2308  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-rn 4299  df-fun 4847
This theorem is referenced by: (None)
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