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| Mirrors > Home > MPE Home > Th. List > sylibr | Structured version Visualization version GIF version | ||
| Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by NM, 3-Jan-1993.) |
| Ref | Expression |
|---|---|
| sylibr.1 | ⊢ (𝜑 → 𝜓) |
| sylibr.2 | ⊢ (𝜒 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| sylibr | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sylibr.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | sylibr.2 | . . 3 ⊢ (𝜒 ↔ 𝜓) | |
| 3 | 2 | biimpri 228 | . 2 ⊢ (𝜓 → 𝜒) |
| 4 | 1, 3 | syl 17 | 1 ⊢ (𝜑 → 𝜒) |
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