Theorem xordi 865

Description: Conjunction distributes over exclusive-or, using -. (ph <-> ps) to express exclusive-or. This is one way to interpret the distributive law of multiplication over addition in modulo 2 arithmetic. (Contributed by NM, 3-Oct-2008.)

Assertion

Ref	Expression
xordi	|- ((ph /\ -. (ps <-> ch)) <-> -. ((ph /\ ps) <-> (ph /\ ch)))

Proof of Theorem xordi

Step	Hyp	Ref	Expression
1		annim 414	. 2 |- ((ph /\ -. (ps <-> ch)) <-> -. (ph -> (ps <-> ch)))
2		pm5.32 617	. 2 |- ((ph -> (ps <-> ch)) <-> ((ph /\ ps) <-> (ph /\ ch)))
3	1, 2	xchbinx 301	1 |- ((ph /\ -. (ps <-> ch)) <-> -. ((ph /\ ps) <-> (ph /\ ch)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by: (None)