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Mirrors > Home > MPE Home > Th. List > Mathboxes > sylibda | Structured version Visualization version GIF version |
Description: A syllogism deduction. (Contributed by SN, 16-Jul-2024.) |
Ref | Expression |
---|---|
sylibda.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
sylibda.2 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
sylibda | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylibda.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | biimpa 481 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
3 | sylibda.2 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
4 | 2, 3 | syldan 595 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∧ wa 400 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 df-an 401 |
This theorem is referenced by: fsuppssind 39772 |
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