Theorem bdaydm 28014

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 28013	. 2 ⊢ bday Fn No
2	1	fndmi 6636	1 ⊢ dom bday = No

This proof depends on syntax axioms:   = wceq 1570  dom cdm 5655   No csur 27876   bday cbday 27878

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 7736

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 8455  df-no 27879  df-bday 27881

This theorem is used by:  nobdaymin  28018  nocvxminlem  28019  bday0  28076  leftval  28114  rightval  28115  madebdayim  28153  lrold  28162  addbdaylem  28282  negbdaylem  28321  oncutlt  28529  oniso  28536  bdayons  28541  bdayn0sf1o  28635