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| Mirrors > Home > MPE Home > Th. List > syl5 | Structured version Visualization version GIF version | ||
| Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. (Contributed by NM, 27-Dec-1992.) (Proof shortened by Wolf Lammen, 25-May-2013.) |
| Ref | Expression |
|---|---|
| syl5.1 | ⊢ (𝜑 → 𝜓) |
| syl5.2 | ⊢ (𝜒 → (𝜓 → 𝜃)) |
| Ref | Expression |
|---|---|
| syl5 | ⊢ (𝜒 → (𝜑 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl5.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | syl5.2 | . . 3 ⊢ (𝜒 → (𝜓 → 𝜃)) | |
| 3 | 1, 2 | syl5com 31 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) |
| 4 | 3 | com12 32 | 1 ⊢ (𝜒 → (𝜑 → 𝜃)) |
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