Theorem pm5.15 933

Description: Theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 15-Oct-2013.)

Assertion

Ref	Expression
pm5.15	|- ( ( ph <-> ps ) \/ ( ph <-> -. ps ) )

Proof of Theorem pm5.15

Step	Hyp	Ref	Expression
1		xor3 372	. . 3 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )
2	1	biimpi 206	. 2 |- ( -. ( ph <-> ps ) -> ( ph <-> -. ps ) )
3	2	orri 391	1 |- ( ( ph <-> ps ) \/ ( ph <-> -. ps ) )

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

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

This theorem is referenced by:  sbc2or  3444