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

Theorem bdxor 13087
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 13067 . . 3  |- BOUNDED  ( ph  \/  ps )
41, 2ax-bdan 13066 . . . 4  |- BOUNDED  ( ph  /\  ps )
54ax-bdn 13068 . . 3  |- BOUNDED  -.  ( ph  /\  ps )
63, 5ax-bdan 13066 . 2  |- BOUNDED  ( ( ph  \/  ps )  /\  -.  ( ph  /\  ps ) )
7 df-xor 1354 . 2  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
86, 7bd0r 13076 1  |- BOUNDED  ( ph  \/_  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    \/ wo 697    \/_ wxo 1353  BOUNDED wbd 13063
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-bd0 13064  ax-bdan 13066  ax-bdor 13067  ax-bdn 13068
This theorem depends on definitions:  df-bi 116  df-xor 1354
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator