Theorem bdayfn 28014

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 27914	. 2 ⊢ bday : No –onto→On
2		fofn 6792	. 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 6357   Fn wfn 6528  –onto→wfo 6531   No csur 27877   bday cbday 27879

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-10 2178  ax-11 2194  ax-12 2213  ax-ext 2732  ax-sep 5251  ax-pow 5330  ax-pr 5398  ax-un 7737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2100  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-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-pw 4559  df-sn 4585  df-pr 4587  df-op 4591  df-uni 4868  df-br 5104  df-opab 5168  df-mpt 5187  df-id 5550  df-xp 5661  df-rel 5662  df-cnv 5663  df-co 5664  df-dm 5665  df-rn 5666  df-suc 6363  df-fun 6535  df-fn 6536  df-f 6537  df-fo 6539  df-1o 8456  df-no 27880  df-bday 27882

This theorem is used by:  bdaydm  28015  nobdaymin  28019  eqcuts2  28052  cutsun12  28056  cutbdaybnd  28061  cutbdaybnd2  28062  cutbdaylt  28064  bday1  28080  cuteq0  28081  madebdaylemlrcut  28165  sltsbday  28183  cofcut1  28186  cofcutr  28190  lrrecfr  28209  oniso  28537  bdayons  28542  n0bday  28618  bdayn0p1  28635  bdaypw2n0bndlem  28729