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Theorem fnsn 5646
Description: Functionality and domain of the singleton of an ordered pair. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
fnsn.1
fnsn.2
Assertion
Ref Expression
fnsn

Proof of Theorem fnsn
StepHypRef Expression
1 fnsn.1 . 2
2 fnsn.2 . 2
3 fnsng 5640 . 2
41, 2, 3mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  e.wcel 1818   cvv 3109  {csn 4029  <.cop 4035  Fnwfn 5588
This theorem is referenced by:  f1osn  5858  fnsnb  6090  fvsnun2  6107  elixpsn  7528  axdc3lem4  8854  hashf1lem1  12504  axlowdimlem8  24252  axlowdimlem9  24253  axlowdimlem11  24255  axlowdimlem12  24256  eupath2lem3  24979  cvmliftlem4  28733  cvmliftlem5  28734  finixpnum  30038  bnj927  33827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-fun 5595  df-fn 5596
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