Metamath Proof Explorer

Theorem ancrb

Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

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

Proof

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