Theorem bdaydmOLD 27954

Description: Obsolete version of bdaydm 27953 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 27852	. . 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

This proof depends on syntax axioms:   = wceq 1569  dom cdm 5660  Oncon0 6360  ⟶wf 6532  –onto→wfo 6534   No csur 27815   bday cbday 27817

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-10 2175  ax-11 2191  ax-12 2212  ax-ext 2734  ax-sep 5256  ax-pow 5335  ax-pr 5403  ax-un 7734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1104  df-tru 1572  df-fal 1582  df-ex 1809  df-nf 1813  df-sb 2096  df-mo 2566  df-eu 2596  df-clab 2741  df-cleq 2754  df-clel 2837  df-nfc 2911  df-ne 2958  df-ral 3079  df-rex 3089  df-rab 3416  df-v 3456  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 5555  df-xp 5666  df-rel 5667  df-cnv 5668  df-co 5669  df-dm 5670  df-rn 5671  df-suc 6366  df-fun 6538  df-fn 6539  df-f 6540  df-fo 6542  df-1o 8451  df-no 27818  df-bday 27820

This theorem is used by: (None)