Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdcsuc Unicode version

Theorem bdcsuc 14717
Description: The successor of a setvar is a bounded class. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcsuc  |- BOUNDED  suc  x

Proof of Theorem bdcsuc
StepHypRef Expression
1 bdcv 14685 . . 3  |- BOUNDED  x
2 bdcsn 14707 . . 3  |- BOUNDED  { x }
31, 2bdcun 14699 . 2  |- BOUNDED  ( x  u.  {
x } )
4 df-suc 4373 . 2  |-  suc  x  =  ( x  u. 
{ x } )
53, 4bdceqir 14681 1  |- BOUNDED  suc  x
Colors of variables: wff set class
Syntax hints:    u. cun 3129   {csn 3594   suc csuc 4367  BOUNDED wbdc 14677
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-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14650  ax-bdor 14653  ax-bdeq 14657  ax-bdel 14658  ax-bdsb 14659
This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3135  df-sn 3600  df-suc 4373  df-bdc 14678
This theorem is referenced by:  bdeqsuc  14718
  Copyright terms: Public domain W3C validator