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

Theorem ordsucg 4194
Description: The successor of an ordinal class is ordinal. (Contributed by Jim Kingdon, 20-Nov-2018.)
Assertion
Ref Expression
ordsucg  _V  Ord  Ord  suc

Proof of Theorem ordsucg
StepHypRef Expression
1 ordsucim 4192 . 2  Ord  Ord  suc
2 sucidg 4119 . . 3  _V  suc
3 ordelord 4084 . . . 4  Ord  suc  suc  Ord
43ex 108 . . 3  Ord 
suc  suc  Ord
52, 4syl5com 26 . 2  _V  Ord  suc  Ord
61, 5impbid2 131 1  _V  Ord  Ord  suc
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wcel 1390   _Vcvv 2551   Ord word 4065   suc csuc 4068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-uni 3572  df-tr 3846  df-iord 4069  df-suc 4074
This theorem is referenced by:  sucelon  4195
  Copyright terms: Public domain W3C validator