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| Mirrors > Home > MPE Home > Th. List > biimpi | Structured version Visualization version GIF version | ||
| Description: Infer an implication from a logical equivalence. Inference associated with biimp 215. (Contributed by NM, 29-Dec-1992.) |
| Ref | Expression |
|---|---|
| biimpi.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| biimpi | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpi.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | biimp 215 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → 𝜓) |
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