Theorem bdaydm 27839

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 27838	. 2 ⊢ bday Fn No
2	1	fndmi 6625	1 ⊢ dom bday = No

Syntax hints:   = wceq 1560  dom cdm 5647   No csur 27701   bday cbday 27703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-10 2175  ax-11 2191  ax-12 2212  ax-ext 2734  ax-sep 5246  ax-pow 5322  ax-pr 5390  ax-un 7718

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1100  df-tru 1563  df-fal 1573  df-ex 1800  df-nf 1804  df-sb 2091  df-mo 2566  df-eu 2596  df-clab 2741  df-cleq 2754  df-clel 2837  df-nfc 2911  df-ne 2958  df-ral 3077  df-rex 3087  df-rab 3415  df-v 3456  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4481  df-pw 4557  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-opab 5163  df-mpt 5182  df-id 5542  df-xp 5653  df-rel 5654  df-cnv 5655  df-co 5656  df-dm 5657  df-rn 5658  df-suc 6352  df-fun 6523  df-fn 6524  df-f 6525  df-fo 6527  df-1o 8437  df-no 27704  df-bday 27706

This theorem is referenced by:  nobdaymin  27843  nocvxminlem  27844  bday0  27901  leftval  27939  rightval  27940  madebdayim  27978  lrold  27987  addbdaylem  28107  negbdaylem  28146  oncutlt  28354  oniso  28361  bdayons  28366  bdayn0sf1o  28460