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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 4396 . 2 ∅ ⊆ {⟨∅, ∅⟩}
2 0ex 5307 . . 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 3948  c0 4322  {csn 4628  cop 4634  Fun wfun 6537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702  ax-sep 5299  ax-nul 5306  ax-pr 5427
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-mo 2533  df-clab 2709  df-cleq 2723  df-clel 2809  df-ral 3061  df-rex 3070  df-rab 3432  df-v 3475  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-fun 6545
This theorem is referenced by:  funcnv0  6614  fn0  6681  0fsupp  9391  strle1  17098  lubfun  18315  glbfun  18328  1pthdlem1  29822  fineqvac  34562
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