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Theorem xorcom 1349
Description:  \/_ is commutative. (Contributed by David A. Wheeler, 6-Oct-2018.)
Assertion
Ref Expression
xorcom  |-  ( (
ph  \/_  ps )  <->  ( ps  \/_  ph ) )

Proof of Theorem xorcom
StepHypRef Expression
1 orcom 700 . . 3  |-  ( (
ph  \/  ps )  <->  ( ps  \/  ph )
)
2 ancom 264 . . . 4  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
32notbii 640 . . 3  |-  ( -.  ( ph  /\  ps ) 
<->  -.  ( ps  /\  ph ) )
41, 3anbi12i 453 . 2  |-  ( ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) )  <->  ( ( ps  \/  ph )  /\  -.  ( ps  /\  ph ) ) )
5 df-xor 1337 . 2  |-  ( (
ph  \/_  ps )  <->  ( ( ph  \/  ps )  /\  -.  ( ph  /\ 
ps ) ) )
6 df-xor 1337 . 2  |-  ( ( ps  \/_  ph )  <->  ( ( ps  \/  ph )  /\  -.  ( ps  /\  ph ) ) )
74, 5, 63bitr4i 211 1  |-  ( (
ph  \/_  ps )  <->  ( ps  \/_  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    <-> wb 104    \/ wo 680    \/_ wxo 1336
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-in1 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-xor 1337
This theorem is referenced by:  rpnegap  9422
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