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

Theorem xordi 895
Description: Conjunction distributes over exclusive-or, using to express exclusive-or. This is one way to interpret the distributive law of multiplication over addition in modulo 2 arithmetic. This is not necessarily true in intuitionistic logic, though anxordi 1378 does hold in it. (Contributed by NM, 3-Oct-2008.)
Assertion
Ref Expression
xordi

Proof of Theorem xordi
StepHypRef Expression
1 annim 425 . 2
2 pm5.32 636 . 2
31, 2xchbinx 310 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369
This theorem is referenced by:  anxordi  1378
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 185  df-an 371
  Copyright terms: Public domain W3C validator