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

Theorem bdcun 13204
 Description: The union of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdcdif.1 BOUNDED
bdcdif.2 BOUNDED
Assertion
Ref Expression
bdcun BOUNDED

Proof of Theorem bdcun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcdif.1 . . . . 5 BOUNDED
21bdeli 13188 . . . 4 BOUNDED
3 bdcdif.2 . . . . 5 BOUNDED
43bdeli 13188 . . . 4 BOUNDED
52, 4ax-bdor 13158 . . 3 BOUNDED
65bdcab 13191 . 2 BOUNDED
7 df-un 3075 . 2
86, 7bdceqir 13186 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wo 697   wcel 1480  cab 2125   cun 3069  BOUNDED wbdc 13182 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-bd0 13155  ax-bdor 13158  ax-bdsb 13164 This theorem depends on definitions:  df-bi 116  df-clab 2126  df-cleq 2132  df-clel 2135  df-un 3075  df-bdc 13183 This theorem is referenced by:  bdcpr  13213  bdctp  13214  bdcsuc  13222
 Copyright terms: Public domain W3C validator