Theorem pm5.24 865

Description: Theorem *5.24 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.24	|- ( -. ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )

Proof of Theorem pm5.24

Step	Hyp	Ref	Expression
1		xor 862	. 2 |- ( -. ( ph <-> ps ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )
2		dfbi3 864	. 2 |- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) )
3	1, 2	xchnxbi 300	1 |- ( -. ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )

Syntax hints:   -. wn 3   <-> wb 177   \/ wo 358   /\ wa 359

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361