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| Mirrors > Home > MPE Home > Th. List > biimpri | Structured version Visualization version GIF version | ||
| Description: Infer a converse implication from a logical equivalence. Inference associated with biimpr 220. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 16-Sep-2013.) |
| Ref | Expression |
|---|---|
| biimpri.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| biimpri | ⊢ (𝜓 → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpri.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | bicomi 224 | . 2 ⊢ (𝜓 ↔ 𝜑) |
| 3 | 2 | biimpi 216 | 1 ⊢ (𝜓 → 𝜑) |
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