Theorem pm5.24 996

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 935	. 2 |- ( -. ( ph <-> ps ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )
2		dfbi3 994	. 2 |- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) )
3	1, 2	xchnxbi 322	1 |- ( -. ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  4exmid  997