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Theorem bdayfn 27833
Description: The birthday function is a function over No . (Contributed by Scott Fenton, 30-Jun-2011.)
Assertion
Ref Expression
bdayfn bday Fn No

Proof of Theorem bdayfn
StepHypRef Expression
1 bdayfo 27737 . 2 bday : No onto→On
2 fofn 6823 . 2 ( bday : No onto→On → bday Fn No )
31, 2ax-mp 5 1 bday Fn No
Colors of variables: wff setvar class
Syntax hints:  Oncon0 6386   Fn wfn 6558  ontowfo 6561   No csur 27699   bday cbday 27701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pow 5371  ax-pr 5438  ax-un 7754
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-pw 4607  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-mpt 5232  df-id 5583  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-dm 5699  df-rn 5700  df-suc 6392  df-fun 6565  df-fn 6566  df-f 6567  df-fo 6569  df-1o 8505  df-no 27702  df-bday 27704
This theorem is referenced by:  nocvxmin  27838  eqscut2  27866  scutun12  27870  scutbdaybnd  27875  scutbdaybnd2  27876  scutbdaylt  27878  bday1s  27891  cuteq0  27892  madebdaylemlrcut  27952  cofcut1  27969  cofcutr  27973  lrrecfr  27991  n0sbday  28369  pw2bday  28433  zs12bday  28439
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