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Theorem frgra0 30539
Description: Any empty graph (graph without vertices) is a friendship graph. (Contributed by Alexander van der Vekens, 30-Sep-2017.)
Assertion
Ref Expression
frgra0  |-  (/) FriendGrph  (/)

Proof of Theorem frgra0
StepHypRef Expression
1 eqid 2438 . 2  |-  (/)  =  (/)
2 frgra0v 30538 . 2  |-  ( (/) FriendGrph  (/)  <->  (/)  =  (/) )
31, 2mpbir 209 1  |-  (/) FriendGrph  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369   (/)c0 3632   class class class wbr 4287   FriendGrph cfrgra 30533
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419  ax-sep 4408  ax-nul 4416  ax-pr 4526
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2256  df-mo 2257  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2715  df-rex 2716  df-reu 2717  df-rab 2719  df-v 2969  df-dif 3326  df-un 3328  df-in 3330  df-ss 3337  df-nul 3633  df-if 3787  df-pw 3857  df-sn 3873  df-pr 3875  df-op 3879  df-br 4288  df-opab 4346  df-id 4631  df-xp 4841  df-rel 4842  df-cnv 4843  df-co 4844  df-dm 4845  df-rn 4846  df-fun 5415  df-fn 5416  df-f 5417  df-f1 5418  df-usgra 23217  df-frgra 30534
This theorem is referenced by: (None)
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