Metamath Proof Explorer

Theorem pm5.3

Description: Theorem *5.3 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)

Ref Expression
Assertion pm5.3 
|- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )

Proof

Step Hyp Ref Expression
1 simpl 
 |-  ( ( ph /\ ps ) -> ph )
2 1 biantrurd 
 |-  ( ( ph /\ ps ) -> ( ch <-> ( ph /\ ch ) ) )
3 2 pm5.74i 
 |-  ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ ps ) -> ( ph /\ ch ) ) )