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

Theorem bdxor 11070
Description: The exclusive disjunction of two bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdxor.1  |- BOUNDED  ph
bdxor.2  |- BOUNDED  ps
Assertion
Ref Expression
bdxor  |- BOUNDED  ( ph  \/_  ps )

Proof of Theorem bdxor
StepHypRef Expression
1 bdxor.1 . . . 4  |- BOUNDED  ph
2 bdxor.2 . . . 4  |- BOUNDED  ps
31, 2ax-bdor 11050 . . 3  |- BOUNDED  ( ph  \/  ps )
41, 2ax-bdan 11049 . . . 4  |- BOUNDED  ( ph  /\  ps )
54ax-bdn 11051 . . 3  |- BOUNDED  -.  ( ph  /\  ps )
63, 5ax-bdan 11049 . 2  |- BOUNDED  ( ( ph  \/  ps )  /\  -.  ( ph  /\  ps ) )
7 df-xor 1308 . 2  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
86, 7bd0r 11059 1  |- BOUNDED  ( ph  \/_  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    \/ wo 662    \/_ wxo 1307  BOUNDED wbd 11046
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11047  ax-bdan 11049  ax-bdor 11050  ax-bdn 11051
This theorem depends on definitions:  df-bi 115  df-xor 1308
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator