Description: Deduction adding an antecedent to both sides of a logical equivalence. (Contributed by NM, 11-May-1993)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | imbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| Assertion | imbi2d | |- ( ph -> ( ( th -> ps ) <-> ( th -> ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imbid.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| 2 | 1 | a1d | |- ( ph -> ( th -> ( ps <-> ch ) ) ) |
| 3 | 2 | pm5.74d | |- ( ph -> ( ( th -> ps ) <-> ( th -> ch ) ) ) |