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Theorem alephfnon 7692
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 6431 . 2  |-  rec (har ,  om )  Fn  On
2 df-aleph 7573 . . 3  |-  aleph  =  rec (har ,  om )
32fneq1i 5338 . 2  |-  ( aleph  Fn  On  <->  rec (har ,  om )  Fn  On )
41, 3mpbir 200 1  |-  aleph  Fn  On
Colors of variables: wff set class
Syntax hints:   Oncon0 4392   omcom 4656    Fn wfn 5250   reccrdg 6422  harchar 7270   alephcale 7569
This theorem is referenced by:  alephon  7696  alephcard  7697  alephnbtwn  7698  alephgeom  7709  alephf1  7712  infenaleph  7718  isinfcard  7719  alephiso  7725  alephsmo  7729  alephf1ALT  7730  alephfplem1  7731  alephfplem3  7733  alephsing  7902  alephadd  8199  alephreg  8204  pwcfsdom  8205  cfpwsdom  8206  gch2  8301  gch3  8302
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-rep 4131  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-reu 2550  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-pss 3168  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-tp 3648  df-op 3649  df-uni 3828  df-iun 3907  df-br 4024  df-opab 4078  df-mpt 4079  df-tr 4114  df-eprel 4305  df-id 4309  df-po 4314  df-so 4315  df-fr 4352  df-we 4354  df-ord 4395  df-on 4396  df-suc 4398  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-f1 5260  df-fo 5261  df-f1o 5262  df-fv 5263  df-recs 6388  df-rdg 6423  df-aleph 7573
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