Theorem bdaydm 27942

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 27941	. 2 ⊢ bday Fn No
2	1	fndmi 6639	1 ⊢ dom bday = No

Syntax hints:   = wceq 1570  dom cdm 5661   No csur 27804   bday cbday 27806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-10 2176  ax-11 2192  ax-12 2213  ax-ext 2735  ax-sep 5257  ax-pow 5336  ax-pr 5404  ax-un 7732

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-nf 1814  df-sb 2097  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2838  df-nfc 2912  df-ne 2959  df-ral 3080  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-in 3912  df-ss 3922  df-nul 4287  df-if 4488  df-pw 4564  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-opab 5174  df-mpt 5193  df-id 5556  df-xp 5667  df-rel 5668  df-cnv 5669  df-co 5670  df-dm 5671  df-rn 5672  df-suc 6366  df-fun 6538  df-fn 6539  df-f 6540  df-fo 6542  df-1o 8449  df-no 27807  df-bday 27809

This theorem is referenced by:  nobdaymin  27946  nocvxminlem  27947  bday0  28004  leftval  28042  rightval  28043  madebdayim  28081  lrold  28090  addbdaylem  28210  negbdaylem  28249  oncutlt  28457  oniso  28464  bdayons  28469  bdayn0sf1o  28563