Metamath Proof Explorer

Theorem pm4.45im

Description: Conjunction with implication. Compare Theorem *4.45 of WhiteheadRussell p. 119. (Contributed by NM, 17-May-1998)

Ref Expression
Assertion pm4.45im 
|- ( ph <-> ( ph /\ ( ps -> ph ) ) )

Proof

Step Hyp Ref Expression
1 ax-1 
 |-  ( ph -> ( ps -> ph ) )
2 1 pm4.71i 
 |-  ( ph <-> ( ph /\ ( ps -> ph ) ) )