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Mirrors > Home > MPE Home > Th. List > sylan2 | 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 |
---|---|
sylan2.1 | ⊢ (𝜑 → 𝜒) |
sylan2.2 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
sylan2 | ⊢ ((𝜓 ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan2.1 | . . 3 ⊢ (𝜑 → 𝜒) | |
2 | 1 | adantl 482 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
3 | sylan2.2 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
4 | 2, 3 | syldan 591 | 1 ⊢ ((𝜓 ∧ 𝜑) → 𝜃) |
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