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Theorem bdayfn 27818
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 27722 . 2 bday : No onto→On
2 fofn 6822 . 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 6384   Fn wfn 6556  ontowfo 6559   No csur 27684   bday cbday 27686
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pow 5365  ax-pr 5432  ax-un 7755
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ne 2941  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-pw 4602  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-mpt 5226  df-id 5578  df-xp 5691  df-rel 5692  df-cnv 5693  df-co 5694  df-dm 5695  df-rn 5696  df-suc 6390  df-fun 6563  df-fn 6564  df-f 6565  df-fo 6567  df-1o 8506  df-no 27687  df-bday 27689
This theorem is referenced by:  nocvxmin  27823  eqscut2  27851  scutun12  27855  scutbdaybnd  27860  scutbdaybnd2  27861  scutbdaylt  27863  bday1s  27876  cuteq0  27877  madebdaylemlrcut  27937  cofcut1  27954  cofcutr  27958  lrrecfr  27976  n0sbday  28354  pw2bday  28418  zs12bday  28424
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