Description: Deduce a converse implication from a logical equivalence. Deduction associated with biimpr and biimpri . (Contributed by NM, 11-Jan-1993) (Proof shortened by Wolf Lammen, 22-Sep-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | biimprd.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| Assertion | biimprd | |- ( ph -> ( ch -> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimprd.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| 2 | id | |- ( ch -> ch ) |
|
| 3 | 2 1 | syl5ibr | |- ( ph -> ( ch -> ps ) ) |