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| Mirrors > Home > MPE Home > Th. List > a2d | Structured version Visualization version GIF version | ||
| Description: Deduction distributing an embedded antecedent. Deduction form of ax-2 7. (Contributed by NM, 23-Jun-1994.) |
| Ref | Expression |
|---|---|
| a2d.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| Ref | Expression |
|---|---|
| a2d | ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | a2d.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
| 2 | ax-2 7 | . 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → ((𝜓 → 𝜒) → (𝜓 → 𝜃))) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃))) |
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