Theorem bdayfn 28191

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 28091	. 2 ⊢ bday:No⟶ontoOn
2		fofn 6828	. 2 ⊢ (bday:No⟶ontoOn → bday Fn No)
3	1, 2	ax-mp 5	1 ⊢ bday Fn No

This proof depends on syntax axioms:  Oncon0 6388   Fn wfn 6561  ⟶ontowfo 6564  Nocsur 28054  bdaycbday 28056

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-11 2197  ax-12 2216  ax-ext 2735  ax-sep 5255  ax-pow 5334  ax-pr 5398  ax-un 7783

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 2102  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2839  df-nfc 2913  df-ne 2960  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-pw 4562  df-sn 4589  df-pr 4591  df-op 4841  df-uni 4873  df-br 5109  df-opab 5174  df-mpt 5193  df-id 5553  df-xp 5664  df-rel 5665  df-cnv 5666  df-co 5667  df-dm 5668  df-rn 5669  df-suc 6394  df-fun 6568  df-fn 6569  df-f 6570  df-fo 6572  df-1o 8514  df-no 28057  df-bday 28059

This theorem is used by:  bdaydm  28192  nobdaymin  28196  eqcuts2  28229  cutsun12  28233  cutbdaybnd  28238  cutbdaybnd2  28239  cutbdaylt  28241  bday1  28257  cuteq0  28258  madebdaylemlrcut  28342  sltsbday  28360  cofcut1  28363  cofcutr  28367  lrrecfr  28386  oniso  28714  bdayons  28719  n0bday  28795  bdayn0p1  28812  bdaypw2n0bndlem  28906