MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  xorexmid Structured version   Unicode version

Theorem xorexmid 1419
Description: Exclusive-or variant of the law of the excluded middle (exmid 416). This statement is ancient, going back to at least Stoic logic. This statement does not necessarily hold in intuitionistic logic. (Contributed by David A. Wheeler, 23-Feb-2019.)
Assertion
Ref Expression
xorexmid  |-  ( ph  \/_ 
-.  ph )

Proof of Theorem xorexmid
StepHypRef Expression
1 pm5.19 361 . 2  |-  -.  ( ph 
<->  -.  ph )
2 df-xor 1401 . 2  |-  ( (
ph  \/_  -.  ph )  <->  -.  ( ph  <->  -.  ph )
)
31, 2mpbir 212 1  |-  ( ph  \/_ 
-.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/_ wxo 1400
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-xor 1401
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator