Theorem bdayfn 28143

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

Step	Hyp	Ref	Expression
1		bdayfo 28043	. 2 ⊢ bday:No–onto→On
2		fofn 6803	. 2 ⊢ (bday:No–onto→On → bday Fn No)
3	1, 2	ax-mp 5	1 ⊢ bday Fn No

This proof depends on syntax axioms:  Oncon0 6365   Fn wfn 6538  –onto→wfo 6541  Nocsur 28006  bdaycbday 28008

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2212  ax-ext 2732  ax-sep 5248  ax-pow 5327  ax-pr 5391  ax-un 7755

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-nf 1816  df-sb 2099  df-mo 2564  df-eu 2594  df-clab 2739  df-cleq 2752  df-clel 2835  df-nfc 2909  df-ne 2956  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-ss 3897  df-dif 4046  df-in 4090  df-un 4150  df-nul 4278  df-if 4482  df-pw 4558  df-sn 4585  df-pr 4587  df-op 4835  df-uni 4867  df-br 5103  df-opab 5167  df-mpt 5186  df-id 5546  df-xp 5657  df-rel 5658  df-cnv 5659  df-co 5660  df-dm 5661  df-rn 5662  df-suc 6371  df-fun 6545  df-fn 6546  df-f 6547  df-fo 6549  df-1o 8484  df-no 28009  df-bday 28011

This theorem is used by:  bdaydm  28144  nobdaymin  28148  eqcuts2  28181  cutsun12  28185  cutbdaybnd  28190  cutbdaybnd2  28191  cutbdaylt  28193  bday1  28209  cuteq0  28210  madebdaylemlrcut  28294  sltsbday  28312  cofcut1  28315  cofcutr  28319  lrrecfr  28338  oniso  28666  bdayons  28671  n0bday  28747  bdayn0p1  28764  bdaypw2n0bndlem  28858