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Theorem uslgrav 24464
Description: The classes of vertices and edges of an undirected simple graph with loops are sets. (Contributed by Alexander van der Vekens, 20-Aug-2017.)
Assertion
Ref Expression
uslgrav  |-  ( V USLGrph  E  ->  ( V  e. 
_V  /\  E  e.  _V ) )

Proof of Theorem uslgrav
StepHypRef Expression
1 reluslgra 24461 . . 3  |-  Rel USLGrph
21brrelexi 5049 . 2  |-  ( V USLGrph  E  ->  V  e.  _V )
31brrelex2i 5050 . 2  |-  ( V USLGrph  E  ->  E  e.  _V )
42, 3jca 532 1  |-  ( V USLGrph  E  ->  ( V  e. 
_V  /\  E  e.  _V ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    e. wcel 1819   _Vcvv 3109   class class class wbr 4456   USLGrph cuslg 24456
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457  df-opab 4516  df-xp 5014  df-rel 5015  df-uslgra 24459
This theorem is referenced by:  edguslgra  24469  uslisushgra  24490  uslisumgra  24491
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