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Theorem fldrels 25113
Description: The field of a relation is a set. (Contributed by FL, 23-May-2011.)
Hypothesis
Ref Expression
fldrels.1  |-  X  = 
U. U. R
Assertion
Ref Expression
fldrels  |-  ( R  e.  S  ->  X  e.  _V )

Proof of Theorem fldrels
StepHypRef Expression
1 fldrels.1 . 2  |-  X  = 
U. U. R
2 uniexg 4517 . . 3  |-  ( R  e.  S  ->  U. R  e.  _V )
3 uniexg 4517 . . 3  |-  ( U. R  e.  _V  ->  U.
U. R  e.  _V )
42, 3syl 15 . 2  |-  ( R  e.  S  ->  U. U. R  e.  _V )
51, 4syl5eqel 2367 1  |-  ( R  e.  S  ->  X  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   _Vcvv 2788   U.cuni 3827
This theorem is referenced by:  ubos  25256  mxlelt  25264
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-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  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-rex 2549  df-v 2790  df-uni 3828
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