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Theorem oafnex 6473
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 2755 . . 3  |-  x  e. 
_V
21sucex 4519 . 2  |-  suc  x  e.  _V
3 eqid 2189 . 2  |-  ( x  e.  _V  |->  suc  x
)  =  ( x  e.  _V  |->  suc  x
)
42, 3fnmpti 5366 1  |-  ( x  e.  _V  |->  suc  x
)  Fn  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2752    |-> cmpt 4082   suc csuc 4386    Fn wfn 5233
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4139  ax-pow 4195  ax-pr 4230  ax-un 4454
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-pw 3595  df-sn 3616  df-pr 3617  df-op 3619  df-uni 3828  df-br 4022  df-opab 4083  df-mpt 4084  df-id 4314  df-suc 4392  df-xp 4653  df-rel 4654  df-cnv 4655  df-co 4656  df-dm 4657  df-fun 5240  df-fn 5241
This theorem is referenced by:  fnoa  6476  oaexg  6477  oav  6483  oav2  6492  oawordi  6498
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