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Theorem fun0 5643
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 3814 . 2  |-  (/)  C_  { <. (/)
,  (/) >. }
2 0ex 4577 . . 3  |-  (/)  e.  _V
32, 2funsn 5634 . 2  |-  Fun  { <.
(/) ,  (/) >. }
4 funss 5604 . 2  |-  ( (/)  C_ 
{ <. (/) ,  (/) >. }  ->  ( Fun  { <. (/) ,  (/) >. }  ->  Fun  (/) ) )
51, 3, 4mp2 9 1  |-  Fun  (/)
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3476   (/)c0 3785   {csn 4027   <.cop 4033   Fun wfun 5580
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-fun 5588
This theorem is referenced by:  fn0  5698  f10  5845  0fsupp  7847  strlemor0  14577  strle1  14582  lubfun  15463  glbfun  15476  0trl  24224  0pth  24248  1pthonlem1  24267
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