Theorem pm4.82

Description: Theorem *4.82 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm4.82	|- ( ( ( ph -> ps ) /\ ( ph -> -. ps ) ) <-> -. ph )

Proof

Step	Hyp	Ref	Expression
1		pm2.65	|- ( ( ph -> ps ) -> ( ( ph -> -. ps ) -> -. ph ) )
2	1	imp	|- ( ( ( ph -> ps ) /\ ( ph -> -. ps ) ) -> -. ph )
3		pm2.21	|- ( -. ph -> ( ph -> ps ) )
4		pm2.21	|- ( -. ph -> ( ph -> -. ps ) )
5	3 4	jca	|- ( -. ph -> ( ( ph -> ps ) /\ ( ph -> -. ps ) ) )
6	2 5	impbii	|- ( ( ( ph -> ps ) /\ ( ph -> -. ps ) ) <-> -. ph )