Theorem bdaydm 28144

Description: The birthday function's domain is No. (Contributed by Scott Fenton, 14-Jun-2011.) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026.)

Assertion

Ref	Expression
bdaydm	⊢ dom bday = No

Proof of Theorem bdaydm

Step	Hyp	Ref	Expression
1		bdayfn 28143	. 2 ⊢ bday Fn No
2	1	fndmi 6648	1 ⊢ dom bday = No

This proof depends on syntax axioms:   = wceq 1569  dom cdm 5651  Nocsur 28006  bdaycbday 28008

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2212  ax-ext 2732  ax-sep 5248  ax-pow 5327  ax-pr 5391  ax-un 7755

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-nf 1816  df-sb 2099  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-ss 3897  df-dif 4046  df-in 4090  df-un 4150  df-nul 4278  df-if 4482  df-pw 4558  df-sn 4585  df-pr 4587  df-op 4835  df-uni 4867  df-br 5103  df-opab 5167  df-mpt 5186  df-id 5546  df-xp 5657  df-rel 5658  df-cnv 5659  df-co 5660  df-dm 5661  df-rn 5662  df-suc 6371  df-fun 6545  df-fn 6546  df-f 6547  df-fo 6549  df-1o 8483  df-no 28009  df-bday 28011

This theorem is used by:  nobdaymin  28148  nocvxminlem  28149  bday0  28206  leftval  28244  rightval  28245  madebdayim  28283  lrold  28292  addbdaylem  28412  negbdaylem  28451  oncutlt  28659  oniso  28666  bdayons  28671  bdayn0sf1o  28765