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Theorem fun0 6632
Description: The empty set is a function. Theorem 10.3 of [Quine] p. 65. (Contributed by NM, 7-Apr-1998.)
Assertion
Ref Expression
fun0 Fun ∅

Proof of Theorem fun0
StepHypRef Expression
1 0ss 4405 . 2 ∅ ⊆ {⟨∅, ∅⟩}
2 0ex 5312 . . 3 ∅ ∈ V
32, 2funsn 6620 . 2 Fun {⟨∅, ∅⟩}
4 funss 6586 . 2 (∅ ⊆ {⟨∅, ∅⟩} → (Fun {⟨∅, ∅⟩} → Fun ∅))
51, 3, 4mp2 9 1 Fun ∅
Colors of variables: wff setvar class
Syntax hints:  wss 3962  c0 4338  {csn 4630  cop 4636  Fun wfun 6556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pr 5437
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-mo 2537  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-br 5148  df-opab 5210  df-id 5582  df-xp 5694  df-rel 5695  df-cnv 5696  df-co 5697  df-fun 6564
This theorem is referenced by:  funcnv0  6633  fn0  6699  0fsupp  9427  strle1  17191  lubfun  18409  glbfun  18422  1pthdlem1  30163  fineqvac  35089
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