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Metamath Proof Explorer

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 )