Theorem bdaydmOLD 28070

Description: Obsolete version of bdaydm 28069 as of 10-Jun-2026. (Contributed by Scott Fenton, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bdaydmOLD	⊢ dom bday = No

Proof of Theorem bdaydmOLD

Step	Hyp	Ref	Expression
1		bdayfo 27968	. . 3 ⊢ bday : No –onto→On
2		fof 6784	. . 3 ⊢ ( bday : No –onto→On → bday : No ⟶On)
3	1, 2	ax-mp 5	. 2 ⊢ bday : No ⟶On
4	3	fdmi 6709	1 ⊢ dom bday = No

This proof depends on syntax axioms:   = wceq 1570  dom cdm 5647  Oncon0 6351  ⟶wf 6523  –onto→wfo 6525   No csur 27931   bday cbday 27933

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 5248  ax-pow 5326  ax-pr 5390  ax-un 7734

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 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4279  df-if 4482  df-pw 4558  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5103  df-opab 5167  df-mpt 5186  df-id 5542  df-xp 5653  df-rel 5654  df-cnv 5655  df-co 5656  df-dm 5657  df-rn 5658  df-suc 6357  df-fun 6529  df-fn 6530  df-f 6531  df-fo 6533  df-1o 8454  df-no 27934  df-bday 27936

This theorem is used by: (None)