Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 10-Feb-2005)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | pm4.71rd.1 | |- ( ph -> ( ps -> ch ) ) |
|
| Assertion | pm4.71rd | |- ( ph -> ( ps <-> ( ch /\ ps ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm4.71rd.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | 1 | pm4.71d | |- ( ph -> ( ps <-> ( ps /\ ch ) ) ) |
| 3 | 2 | biancomd | |- ( ph -> ( ps <-> ( ch /\ ps ) ) ) |