Theorem bdayfn 27906

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 27806	. 2 ⊢ bday : No –onto→On
2		fofn 6795	. 2 ⊢ ( bday : No –onto→On → bday Fn No )
3	1, 2	ax-mp 5	1 ⊢ bday Fn No

Syntax hints:  Oncon0 6361   Fn wfn 6532  –onto→wfo 6535   No csur 27769   bday cbday 27771

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-10 2182  ax-11 2198  ax-12 2219  ax-ext 2741  ax-sep 5261  ax-pow 5337  ax-pr 5405  ax-un 7733

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-nf 1811  df-sb 2098  df-mo 2573  df-eu 2603  df-clab 2748  df-cleq 2761  df-clel 2844  df-nfc 2918  df-ne 2965  df-ral 3086  df-rex 3096  df-rab 3424  df-v 3465  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4295  df-if 4493  df-pw 4569  df-sn 4595  df-pr 4597  df-op 4601  df-uni 4877  df-br 5114  df-opab 5178  df-mpt 5197  df-id 5557  df-xp 5668  df-rel 5669  df-cnv 5670  df-co 5671  df-dm 5672  df-rn 5673  df-suc 6367  df-fun 6539  df-fn 6540  df-f 6541  df-fo 6543  df-1o 8452  df-no 27772  df-bday 27774

This theorem is referenced by:  bdaydm  27907  nobdaymin  27911  eqcuts2  27944  cutsun12  27948  cutbdaybnd  27953  cutbdaybnd2  27954  cutbdaylt  27956  bday1  27972  cuteq0  27973  madebdaylemlrcut  28057  sltsbday  28075  cofcut1  28078  cofcutr  28082  lrrecfr  28101  oniso  28429  bdayons  28434  n0bday  28510  bdayn0p1  28527  bdaypw2n0bndlem  28621