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Metamath Proof Explorer

Theorem pm3.31

Description: Theorem *3.31 (Imp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 24-Mar-2013)

Ref Expression
Assertion pm3.31 
|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph /\ ps ) -> ch ) )

Proof

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