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Mirrors > Home > MPE Home > Th. List > sylanb | Structured version Visualization version GIF version |
Description: A syllogism inference. (Contributed by NM, 18-May-1994.) |
Ref | Expression |
---|---|
sylanb.1 | ⊢ (𝜑 ↔ 𝜓) |
sylanb.2 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
sylanb | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylanb.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | biimpi 205 | . 2 ⊢ (𝜑 → 𝜓) |
3 | sylanb.2 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
4 | 2, 3 | sylan 487 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
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