Metamath Proof Explorer
Description: This used to be in the main part. (Contributed by Wolf Lammen, 14-May-2013) (Revised by BJ, 14-Jun-2019)
|
|
Ref |
Expression |
|
Assertion |
bj-bisym |
⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → 𝜃 ) ) → ( ( ( 𝜓 → 𝜑 ) → ( 𝜃 → 𝜒 ) ) → ( ( 𝜑 ↔ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
impbi |
⊢ ( ( 𝜒 → 𝜃 ) → ( ( 𝜃 → 𝜒 ) → ( 𝜒 ↔ 𝜃 ) ) ) |
| 2 |
1
|
bj-bi3ant |
⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → 𝜃 ) ) → ( ( ( 𝜓 → 𝜑 ) → ( 𝜃 → 𝜒 ) ) → ( ( 𝜑 ↔ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) ) ) ) |