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Theorem oafnex 6439
Description: The characteristic function for ordinal addition is defined everywhere. (Contributed by Jim Kingdon, 27-Jul-2019.)
Assertion
Ref Expression
oafnex  |-  ( x  e.  _V  |->  suc  x
)  Fn  _V

Proof of Theorem oafnex
StepHypRef Expression
1 vex 2740 . . 3  |-  x  e. 
_V
21sucex 4495 . 2  |-  suc  x  e.  _V
3 eqid 2177 . 2  |-  ( x  e.  _V  |->  suc  x
)  =  ( x  e.  _V  |->  suc  x
)
42, 3fnmpti 5340 1  |-  ( x  e.  _V  |->  suc  x
)  Fn  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2737    |-> cmpt 4061   suc csuc 4362    Fn wfn 5207
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-pow 4171  ax-pr 4206  ax-un 4430
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-pw 3576  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-opab 4062  df-mpt 4063  df-id 4290  df-suc 4368  df-xp 4629  df-rel 4630  df-cnv 4631  df-co 4632  df-dm 4633  df-fun 5214  df-fn 5215
This theorem is referenced by:  fnoa  6442  oaexg  6443  oav  6449  oav2  6458  oawordi  6464
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