Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of WhiteheadRussell p. 120 (with conjunct reversed). (Contributed by NM, 1-Dec-2003)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | pm4.71ri.1 | |- ( ph -> ps ) |
|
| Assertion | pm4.71ri | |- ( ph <-> ( ps /\ ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm4.71ri.1 | |- ( ph -> ps ) |
|
| 2 | 1 | pm4.71i | |- ( ph <-> ( ph /\ ps ) ) |
| 3 | 2 | biancomi | |- ( ph <-> ( ps /\ ph ) ) |