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Theorem fun0 6613
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 4393 . 2 ∅ ⊆ {⟨∅, ∅⟩}
2 0ex 5302 . . 3 ∅ ∈ V
32, 2funsn 6601 . 2 Fun {⟨∅, ∅⟩}
4 funss 6567 . 2 (∅ ⊆ {⟨∅, ∅⟩} → (Fun {⟨∅, ∅⟩} → Fun ∅))
51, 3, 4mp2 9 1 Fun ∅
Colors of variables: wff setvar class
Syntax hints:  wss 3945  c0 4319  {csn 4625  cop 4631  Fun wfun 6537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5294  ax-nul 5301  ax-pr 5424
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-mo 2530  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3058  df-rex 3067  df-rab 3429  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4320  df-if 4526  df-sn 4626  df-pr 4628  df-op 4632  df-br 5144  df-opab 5206  df-id 5571  df-xp 5679  df-rel 5680  df-cnv 5681  df-co 5682  df-fun 6545
This theorem is referenced by:  funcnv0  6614  fn0  6681  0fsupp  9408  strle1  17121  lubfun  18338  glbfun  18351  1pthdlem1  29939  fineqvac  34712
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