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| Mirrors > Home > MPE Home > Th. List > syl11 | Structured version Visualization version GIF version | ||
| Description: A syllogism inference. Commuted form of an instance of syl 17. (Contributed by BJ, 25-Oct-2021.) |
| Ref | Expression |
|---|---|
| syl11.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| syl11.2 | ⊢ (𝜃 → 𝜑) |
| Ref | Expression |
|---|---|
| syl11 | ⊢ (𝜓 → (𝜃 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl11.2 | . . 3 ⊢ (𝜃 → 𝜑) | |
| 2 | syl11.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | syl 17 | . 2 ⊢ (𝜃 → (𝜓 → 𝜒)) |
| 4 | 3 | com12 32 | 1 ⊢ (𝜓 → (𝜃 → 𝜒)) |
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