Theorem bdaydmOLD 27813

Description: Obsolete version of bdaydm 27812 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 27711	. . 3 ⊢ bday : No –onto→On
2		fof 6767	. . 3 ⊢ ( bday : No –onto→On → bday : No ⟶On)
3	1, 2	ax-mp 5	. 2 ⊢ bday : No ⟶On
4	3	fdmi 6692	1 ⊢ dom bday = No

Syntax hints:   = wceq 1554  dom cdm 5640  Oncon0 6335  ⟶wf 6506  –onto→wfo 6508   No csur 27674   bday cbday 27676

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-10 2169  ax-11 2185  ax-12 2206  ax-ext 2728  ax-sep 5240  ax-pow 5316  ax-pr 5384  ax-un 7707

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-3an 1097  df-tru 1557  df-fal 1567  df-ex 1794  df-nf 1798  df-sb 2085  df-mo 2560  df-eu 2590  df-clab 2735  df-cleq 2748  df-clel 2831  df-nfc 2905  df-ne 2952  df-ral 3071  df-rex 3081  df-rab 3409  df-v 3450  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4281  df-if 4475  df-pw 4551  df-sn 4577  df-pr 4579  df-op 4583  df-uni 4860  df-br 5095  df-opab 5157  df-mpt 5176  df-id 5535  df-xp 5646  df-rel 5647  df-cnv 5648  df-co 5649  df-dm 5650  df-rn 5651  df-suc 6341  df-fun 6512  df-fn 6513  df-f 6514  df-fo 6516  df-1o 8425  df-no 27677  df-bday 27679

This theorem is referenced by: (None)