Metamath Proof Explorer

Theorem pm5.31

Description: Theorem *5.31 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm5.31 
|- ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ( ps /\ ch ) ) )

Proof

Step Hyp Ref Expression
1 simpr 
 |-  ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ps ) )
2 simpl 
 |-  ( ( ch /\ ( ph -> ps ) ) -> ch )
3 1 2 jctird 
 |-  ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ( ps /\ ch ) ) )