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Theorem fun0 5307
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 3483 . 2  |-  (/)  C_  { <. (/)
,  (/) >. }
2 0ex 4150 . . 3  |-  (/)  e.  _V
32, 2funsn 5300 . 2  |-  Fun  { <.
(/) ,  (/) >. }
4 funss 5273 . 2  |-  ( (/)  C_ 
{ <. (/) ,  (/) >. }  ->  ( Fun  { <. (/) ,  (/) >. }  ->  Fun  (/) ) )
51, 3, 4mp2 17 1  |-  Fun  (/)
Colors of variables: wff set class
Syntax hints:    C_ wss 3152   (/)c0 3455   {csn 3640   <.cop 3643   Fun wfun 5249
This theorem is referenced by:  fn0  5363  f10  5507  strlemor0  13234  strle1  13239  0alg  25756
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-fun 5257
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