Metamath Proof Explorer

Theorem 3anbi1d

Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006)

Ref Expression
Hypothesis 3anbi1d.1 
|- ( ph -> ( ps <-> ch ) )
Assertion 3anbi1d 
|- ( ph -> ( ( ps /\ th /\ ta ) <-> ( ch /\ th /\ ta ) ) )

Proof

Step Hyp Ref Expression
1 3anbi1d.1 
 |-  ( ph -> ( ps <-> ch ) )
2 biidd 
 |-  ( ph -> ( th <-> th ) )
3 1 2 3anbi12d 
 |-  ( ph -> ( ( ps /\ th /\ ta ) <-> ( ch /\ th /\ ta ) ) )