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Theorem ranfldrefc 25058
 Description: The range of a reflexive class equals its field. (Contributed by FL, 29-Dec-2011.)
Assertion
Ref Expression
ranfldrefc
Distinct variable group:   ,

Proof of Theorem ranfldrefc
StepHypRef Expression
1 vex 2791 . . . . . . 7
21, 1brelrn 4909 . . . . . 6
32ralimi 2618 . . . . 5
4 df-ral 2548 . . . . 5
53, 4sylib 188 . . . 4
6 dfss2 3169 . . . 4
75, 6sylibr 203 . . 3
8 ssun2 3339 . . 3
97, 8jctil 523 . 2
10 eqss 3194 . 2
119, 10sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1527   wceq 1623   wcel 1684  wral 2543   cun 3150   wss 3152   class class class wbr 4023   cdm 4689   crn 4690 This theorem is referenced by:  dranfldrefc  25059 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-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  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-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700
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