Theorem pm5.15 859

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 346	. . 3 |- (-. (ph <-> ps) <-> (ph <-> -. ps))
2	1	biimpi 186	. 2 |- (-. (ph <-> ps) -> (ph <-> -. ps))
3	2	orri 365	1 |- ((ph <-> ps) \/ (ph <-> -. ps))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357

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-or 359

This theorem is referenced by:  sbc2or  3055