Metamath Proof Explorer

Theorem iba

Description: Introduction of antecedent as conjunct. Theorem *4.73 of WhiteheadRussell p. 121. (Contributed by NM, 30-Mar-1994)

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

Proof

Step Hyp Ref Expression
1 pm3.21 
 |-  ( ph -> ( ps -> ( ps /\ ph ) ) )
2 simpl 
 |-  ( ( ps /\ ph ) -> ps )
3 1 2 impbid1 
 |-  ( ph -> ( ps <-> ( ps /\ ph ) ) )