Metamath Proof Explorer

Theorem pm3.33

Description: Theorem *3.33 (Syll) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm3.33 
|- ( ( ( ph -> ps ) /\ ( ps -> ch ) ) -> ( ph -> ch ) )

Proof

Step Hyp Ref Expression
1 imim1 
 |-  ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
2 1 imp 
 |-  ( ( ( ph -> ps ) /\ ( ps -> ch ) ) -> ( ph -> ch ) )