ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  oafnex GIF version

Theorem oafnex 6054
Description: The characteristic function for ordinal addition is defined everywhere. (Contributed by Jim Kingdon, 27-Jul-2019.)
Assertion
Ref Expression
oafnex (𝑥 ∈ V ↦ suc 𝑥) Fn V

Proof of Theorem oafnex
StepHypRef Expression
1 vex 2577 . . 3 𝑥 ∈ V
21sucex 4252 . 2 suc 𝑥 ∈ V
3 eqid 2056 . 2 (𝑥 ∈ V ↦ suc 𝑥) = (𝑥 ∈ V ↦ suc 𝑥)
42, 3fnmpti 5054 1 (𝑥 ∈ V ↦ suc 𝑥) Fn V
Colors of variables: wff set class
Syntax hints:  Vcvv 2574  cmpt 3845  suc csuc 4129   Fn wfn 4924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-13 1420  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3902  ax-pow 3954  ax-pr 3971  ax-un 4197
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2949  df-in 2951  df-ss 2958  df-pw 3388  df-sn 3408  df-pr 3409  df-op 3411  df-uni 3608  df-br 3792  df-opab 3846  df-mpt 3847  df-id 4057  df-suc 4135  df-xp 4378  df-rel 4379  df-cnv 4380  df-co 4381  df-dm 4382  df-fun 4931  df-fn 4932
This theorem is referenced by:  fnoa  6057  oaexg  6058  oav  6064  oacl  6070  oav2  6073  oawordi  6079
  Copyright terms: Public domain W3C validator