Description: Deduction adding a left conjunct to both sides of a logical equivalence. (Contributed by NM, 11-May-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | anbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| Assertion | anbi2d | |- ( ph -> ( ( th /\ ps ) <-> ( th /\ ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| 2 | 1 | a1d | |- ( ph -> ( th -> ( ps <-> ch ) ) ) |
| 3 | 2 | pm5.32d | |- ( ph -> ( ( th /\ ps ) <-> ( th /\ ch ) ) ) |