Metamath Proof Explorer

Theorem anabs5

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 9-Dec-2012)

Ref Expression
Assertion anabs5 
|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )

Proof

Step Hyp Ref Expression
1 ibar 
 |-  ( ph -> ( ps <-> ( ph /\ ps ) ) )
2 1 bicomd 
 |-  ( ph -> ( ( ph /\ ps ) <-> ps ) )
3 2 pm5.32i 
 |-  ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )