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Theorem alephfnon 7951
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 6679 . 2  |-  rec (har ,  om )  Fn  On
2 df-aleph 7832 . . 3  |-  aleph  =  rec (har ,  om )
32fneq1i 5542 . 2  |-  ( aleph  Fn  On  <->  rec (har ,  om )  Fn  On )
41, 3mpbir 202 1  |-  aleph  Fn  On
Colors of variables: wff set class
Syntax hints:   Oncon0 4584   omcom 4848    Fn wfn 5452   reccrdg 6670  harchar 7527   alephcale 7828
This theorem is referenced by:  alephon  7955  alephcard  7956  alephnbtwn  7957  alephgeom  7968  alephf1  7971  infenaleph  7977  isinfcard  7978  alephiso  7984  alephsmo  7988  alephf1ALT  7989  alephfplem1  7990  alephfplem3  7992  alephsing  8161  alephadd  8457  alephreg  8462  pwcfsdom  8463  cfpwsdom  8464  gch2  8555  gch3  8556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4323  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-iun 4097  df-br 4216  df-opab 4270  df-mpt 4271  df-tr 4306  df-eprel 4497  df-id 4501  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588  df-suc 4590  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-recs 6636  df-rdg 6671  df-aleph 7832
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