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Theorem r1fnon 7628
Description: The cumulative hierarchy of sets function is a function on the class of ordinal numbers. (Contributed by NM, 5-Oct-2003.) (Revised by Mario Carneiro, 10-Sep-2013.)
Assertion
Ref Expression
r1fnon  |-  R1  Fn  On

Proof of Theorem r1fnon
StepHypRef Expression
1 rdgfnon 6614 . 2  |-  rec (
( x  e.  _V  |->  ~P x ) ,  (/) )  Fn  On
2 df-r1 7625 . . 3  |-  R1  =  rec ( ( x  e. 
_V  |->  ~P x ) ,  (/) )
32fneq1i 5481 . 2  |-  ( R1  Fn  On  <->  rec (
( x  e.  _V  |->  ~P x ) ,  (/) )  Fn  On )
41, 3mpbir 201 1  |-  R1  Fn  On
Colors of variables: wff set class
Syntax hints:   _Vcvv 2901   (/)c0 3573   ~Pcpw 3744    e. cmpt 4209   Oncon0 4524    Fn wfn 5391   reccrdg 6605   R1cr1 7623
This theorem is referenced by:  r1suc  7631  r1lim  7633  r111  7636  r1ord  7641  r1ord3  7643  r1elss  7667  jech9.3  7675  onwf  7691  ssrankr1  7696  r1val3  7699  r1pw  7706  rankuni  7724  rankr1b  7725  r1om  8059  hsmexlem6  8246  smobeth  8396  wunr1om  8529  r1limwun  8546  r1wunlim  8547  tskr1om  8577  tskr1om2  8578  inar1  8585  rankcf  8587  inatsk  8588  r1tskina  8592  grur1  8630  grothomex  8639  aomclem4  26825
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 1661  ax-8 1682  ax-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-rep 4263  ax-sep 4273  ax-nul 4281  ax-pow 4320  ax-pr 4346  ax-un 4643
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 2244  df-mo 2245  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-reu 2658  df-rab 2660  df-v 2903  df-sbc 3107  df-csb 3197  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-pss 3281  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-tp 3767  df-op 3768  df-uni 3960  df-iun 4039  df-br 4156  df-opab 4210  df-mpt 4211  df-tr 4246  df-eprel 4437  df-id 4441  df-po 4446  df-so 4447  df-fr 4484  df-we 4486  df-ord 4527  df-on 4528  df-suc 4530  df-xp 4826  df-rel 4827  df-cnv 4828  df-co 4829  df-dm 4830  df-rn 4831  df-res 4832  df-ima 4833  df-iota 5360  df-fun 5398  df-fn 5399  df-f 5400  df-f1 5401  df-fo 5402  df-f1o 5403  df-fv 5404  df-recs 6571  df-rdg 6606  df-r1 7625
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