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Theorem frgra0 26315
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 2610 . 2 ∅ = ∅
2 frgra0v 26314 . 2 (∅ FriendGrph ∅ ↔ ∅ = ∅)
31, 2mpbir 220 1 ∅ FriendGrph ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1475  c0 3874   class class class wbr 4578   FriendGrph cfrgra 26309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4704  ax-nul 4712  ax-pr 4828
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-reu 2903  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-pw 4110  df-sn 4126  df-pr 4128  df-op 4132  df-br 4579  df-opab 4639  df-id 4943  df-xp 5034  df-rel 5035  df-cnv 5036  df-co 5037  df-dm 5038  df-rn 5039  df-fun 5792  df-fn 5793  df-f 5794  df-f1 5795  df-usgra 25656  df-frgra 26310
This theorem is referenced by: (None)
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