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| Mirrors > Home > MPE Home > Th. List > biimprcd | Structured version Visualization version GIF version | ||
| 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 |
|---|---|
| biimpcd.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| biimprcd | ⊢ (𝜒 → (𝜑 → 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ (𝜒 → 𝜒) | |
| 2 | biimpcd.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 3 | 1, 2 | syl5ibrcom 247 | 1 ⊢ (𝜒 → (𝜑 → 𝜓)) |
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