Theorem bdaydmOLD 27919

Description: Obsolete version of bdaydm 27918 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 27817	. . 3 ⊢ bday : No –onto→On
2		fof 6792	. . 3 ⊢ ( bday : No –onto→On → bday : No ⟶On)
3	1, 2	ax-mp 5	. 2 ⊢ bday : No ⟶On
4	3	fdmi 6717	1 ⊢ dom bday = No

Syntax hints:   = wceq 1568  dom cdm 5661  Oncon0 6360  ⟶wf 6532  –onto→wfo 6534   No csur 27780   bday cbday 27782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-10 2174  ax-11 2190  ax-12 2211  ax-ext 2733  ax-sep 5256  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 1103  df-tru 1571  df-fal 1581  df-ex 1808  df-nf 1812  df-sb 2095  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 3415  df-v 3455  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-pw 4563  df-sn 4589  df-pr 4591  df-op 4595  df-uni 4872  df-br 5109  df-opab 5173  df-mpt 5192  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 8452  df-no 27783  df-bday 27785

This theorem is referenced by: (None)