Description: Deduce a converse commuted implication from a logical equivalence. (Contributed by NM, 3-May-1994) (Proof shortened by Wolf Lammen, 20-Dec-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | biimpcd.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| Assertion | biimprcd | |- ( ch -> ( ph -> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpcd.1 | |- ( ph -> ( ps <-> ch ) ) |
|
| 2 | id | |- ( ch -> ch ) |
|
| 3 | 2 1 | syl5ibrcom | |- ( ch -> ( ph -> ps ) ) |