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 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
| Assertion | biimprcd | ⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpcd.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
| 2 | id | ⊢ ( 𝜒 → 𝜒 ) | |
| 3 | 2 1 | syl5ibrcom | ⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) ) |