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Mirrors > Home > MPE Home > Th. List > sylan | Structured version Visualization version GIF version |
Description: A syllogism inference. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Nov-2012.) |
Ref | Expression |
---|---|
sylan.1 | ⊢ (𝜑 → 𝜓) |
sylan.2 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
sylan | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | sylan.2 | . . 3 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
3 | 2 | expcom 417 | . 2 ⊢ (𝜒 → (𝜓 → 𝜃)) |
4 | 1, 3 | mpan9 510 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
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