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Theorem funsn 5300
 Description: A singleton of an ordered pair is a function. Theorem 10.5 of [Quine] p. 65. (Contributed by NM, 12-Aug-1994.)
Hypotheses
Ref Expression
funsn.1
funsn.2
Assertion
Ref Expression
funsn

Proof of Theorem funsn
StepHypRef Expression
1 funsn.1 . 2
2 funsn.2 . 2
3 funsng 5298 . 2
41, 2, 3mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wcel 1684  cvv 2788  csn 3640  cop 3643   wfun 5249 This theorem is referenced by:  funtp  5303  fun0  5307  fvsn  5713  dcomex  8073  axdc3lem4  8079  xpsc0  13462  xpsc1  13463  wfrlem13  24268  1alg  25722  bnj1421  29072 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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