Theorem bdayfn 28134

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 28034	. 2 ⊢ bday : No –onto→On
2		fofn 6798	. 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 6362   Fn wfn 6533  –onto→wfo 6536   No csur 27997   bday cbday 27999

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 2733  ax-sep 5249  ax-pow 5327  ax-pr 5391  ax-un 7751

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 2565  df-eu 2595  df-clab 2740  df-cleq 2753  df-clel 2836  df-nfc 2910  df-ne 2957  df-ral 3078  df-rex 3088  df-rab 3414  df-v 3453  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 5546  df-xp 5657  df-rel 5658  df-cnv 5659  df-co 5660  df-dm 5661  df-rn 5662  df-suc 6368  df-fun 6540  df-fn 6541  df-f 6542  df-fo 6544  df-1o 8476  df-no 28000  df-bday 28002

This theorem is used by:  bdaydm  28135  nobdaymin  28139  eqcuts2  28172  cutsun12  28176  cutbdaybnd  28181  cutbdaybnd2  28182  cutbdaylt  28184  bday1  28200  cuteq0  28201  madebdaylemlrcut  28285  sltsbday  28303  cofcut1  28306  cofcutr  28310  lrrecfr  28329  oniso  28657  bdayons  28662  n0bday  28738  bdayn0p1  28755  bdaypw2n0bndlem  28849