Theorem pm5.16

Description: Theorem *5.16 of WhiteheadRussell p. 124. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 17-Oct-2013)

	Ref	Expression
Assertion	pm5.16	|- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.18	|- ( ( ph <-> ps ) <-> -. ( ph <-> -. ps ) )
2	1	biimpi	|- ( ( ph <-> ps ) -> -. ( ph <-> -. ps ) )
3		imnan	|- ( ( ( ph <-> ps ) -> -. ( ph <-> -. ps ) ) <-> -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) ) )
4	2 3	mpbi	|- -. ( ( ph <-> ps ) /\ ( ph <-> -. ps ) )