Metamath Proof Explorer


Theorem anclb

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of WhiteheadRussell p. 120. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

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

Proof

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