Theorem bdaydm 28128

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 28127	. 2 ⊢ bday Fn No
2	1	fndmi 6641	1 ⊢ dom bday = No

This proof depends on syntax axioms:   = wceq 1570  dom cdm 5651   No csur 27990   bday cbday 27992

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 7749

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 6367  df-fun 6539  df-fn 6540  df-f 6541  df-fo 6543  df-1o 8469  df-no 27993  df-bday 27995

This theorem is used by:  nobdaymin  28132  nocvxminlem  28133  bday0  28190  leftval  28228  rightval  28229  madebdayim  28267  lrold  28276  addbdaylem  28396  negbdaylem  28435  oncutlt  28643  oniso  28650  bdayons  28655  bdayn0sf1o  28749