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Metamath Proof Explorer

Theorem pm3.37

Description: Theorem *3.37 (Transp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 23-Oct-2012)

Ref Expression
Assertion pm3.37 
|- ( ( ( ph /\ ps ) -> ch ) -> ( ( ph /\ -. ch ) -> -. ps ) )

Proof

Step Hyp Ref Expression
1 pm4.14 
 |-  ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ -. ch ) -> -. ps ) )
2 1 biimpi 
 |-  ( ( ( ph /\ ps ) -> ch ) -> ( ( ph /\ -. ch ) -> -. ps ) )