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Theorem alephfnon 8521
Description: The aleph function is a function on the class of ordinal numbers. (Contributed by NM, 21-Oct-2003.) (Revised by Mario Carneiro, 13-Sep-2013.)
Assertion
Ref Expression
alephfnon  |-  aleph  Fn  On

Proof of Theorem alephfnon
StepHypRef Expression
1 rdgfnon 7161 . 2  |-  rec (har ,  om )  Fn  On
2 df-aleph 8399 . . 3  |-  aleph  =  rec (har ,  om )
32fneq1i 5691 . 2  |-  ( aleph  Fn  On  <->  rec (har ,  om )  Fn  On )
41, 3mpbir 214 1  |-  aleph  Fn  On
Colors of variables: wff setvar class
Syntax hints:   Oncon0 5441    Fn wfn 5595   omcom 6718   reccrdg 7152  harchar 8096   alephcale 8395
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-8 1899  ax-9 1906  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441  ax-rep 4528  ax-sep 4538  ax-nul 4547  ax-pow 4594  ax-pr 4652  ax-un 6609
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-3or 992  df-3an 993  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-eu 2313  df-mo 2314  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-ne 2634  df-ral 2753  df-rex 2754  df-reu 2755  df-rab 2757  df-v 3058  df-sbc 3279  df-csb 3375  df-dif 3418  df-un 3420  df-in 3422  df-ss 3429  df-pss 3431  df-nul 3743  df-if 3893  df-sn 3980  df-pr 3982  df-tp 3984  df-op 3986  df-uni 4212  df-iun 4293  df-br 4416  df-opab 4475  df-mpt 4476  df-tr 4511  df-eprel 4763  df-id 4767  df-po 4773  df-so 4774  df-fr 4811  df-we 4813  df-xp 4858  df-rel 4859  df-cnv 4860  df-co 4861  df-dm 4862  df-rn 4863  df-res 4864  df-ima 4865  df-pred 5398  df-ord 5444  df-on 5445  df-suc 5447  df-iota 5564  df-fun 5602  df-fn 5603  df-f 5604  df-f1 5605  df-fo 5606  df-f1o 5607  df-fv 5608  df-wrecs 7053  df-recs 7115  df-rdg 7153  df-aleph 8399
This theorem is referenced by:  alephon  8525  alephcard  8526  alephnbtwn  8527  alephgeom  8538  alephf1  8541  infenaleph  8547  isinfcard  8548  alephiso  8554  alephsmo  8558  alephf1ALT  8559  alephfplem1  8560  alephfplem3  8562  alephsing  8731  alephadd  9027  alephreg  9032  pwcfsdom  9033  cfpwsdom  9034  gch2  9125  gch3  9126
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