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Theorem alephfnon 7910
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 6643 . 2  |-  rec (har ,  om )  Fn  On
2 df-aleph 7791 . . 3  |-  aleph  =  rec (har ,  om )
32fneq1i 5506 . 2  |-  ( aleph  Fn  On  <->  rec (har ,  om )  Fn  On )
41, 3mpbir 201 1  |-  aleph  Fn  On
Colors of variables: wff set class
Syntax hints:   Oncon0 4549   omcom 4812    Fn wfn 5416   reccrdg 6634  harchar 7488   alephcale 7787
This theorem is referenced by:  alephon  7914  alephcard  7915  alephnbtwn  7916  alephgeom  7927  alephf1  7930  infenaleph  7936  isinfcard  7937  alephiso  7943  alephsmo  7947  alephf1ALT  7948  alephfplem1  7949  alephfplem3  7951  alephsing  8120  alephadd  8416  alephreg  8421  pwcfsdom  8422  cfpwsdom  8423  gch2  8518  gch3  8519
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-rep 4288  ax-sep 4298  ax-nul 4306  ax-pow 4345  ax-pr 4371  ax-un 4668
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-reu 2681  df-rab 2683  df-v 2926  df-sbc 3130  df-csb 3220  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-pss 3304  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-tp 3790  df-op 3791  df-uni 3984  df-iun 4063  df-br 4181  df-opab 4235  df-mpt 4236  df-tr 4271  df-eprel 4462  df-id 4466  df-po 4471  df-so 4472  df-fr 4509  df-we 4511  df-ord 4552  df-on 4553  df-suc 4555  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-rn 4856  df-res 4857  df-ima 4858  df-iota 5385  df-fun 5423  df-fn 5424  df-f 5425  df-f1 5426  df-fo 5427  df-f1o 5428  df-fv 5429  df-recs 6600  df-rdg 6635  df-aleph 7791
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