Theorem bdayfn 27941

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 27841	. 2 ⊢ bday : No –onto→On
2		fofn 6794	. 2 ⊢ ( bday : No –onto→On → bday Fn No )
3	1, 2	ax-mp 5	1 ⊢ bday Fn No

Syntax hints:  Oncon0 6360   Fn wfn 6531  –onto→wfo 6534   No csur 27804   bday cbday 27806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-10 2176  ax-11 2192  ax-12 2213  ax-ext 2735  ax-sep 5257  ax-pow 5336  ax-pr 5404  ax-un 7732

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-nf 1814  df-sb 2097  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2838  df-nfc 2912  df-ne 2959  df-ral 3080  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4488  df-pw 4564  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-opab 5174  df-mpt 5193  df-id 5556  df-xp 5667  df-rel 5668  df-cnv 5669  df-co 5670  df-dm 5671  df-rn 5672  df-suc 6366  df-fun 6538  df-fn 6539  df-f 6540  df-fo 6542  df-1o 8449  df-no 27807  df-bday 27809

This theorem is referenced by:  bdaydm  27942  nobdaymin  27946  eqcuts2  27979  cutsun12  27983  cutbdaybnd  27988  cutbdaybnd2  27989  cutbdaylt  27991  bday1  28007  cuteq0  28008  madebdaylemlrcut  28092  sltsbday  28110  cofcut1  28113  cofcutr  28117  lrrecfr  28136  oniso  28464  bdayons  28469  n0bday  28545  bdayn0p1  28562  bdaypw2n0bndlem  28656