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| Mirrors > Home > MPE Home > Th. List > biimpd | Structured version Visualization version GIF version | ||
| Description: Deduce an implication from a logical equivalence. Deduction associated with biimp 215 and biimpi 216. (Contributed by NM, 11-Jan-1993.) |
| Ref | Expression |
|---|---|
| biimpd.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| Ref | Expression |
|---|---|
| biimpd | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimpd.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 2 | biimp 215 | . 2 ⊢ ((𝜓 ↔ 𝜒) → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
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