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| Mirrors > Home > MPE Home > Th. List > impr | Structured version Visualization version GIF version | ||
| Description: Import a wff into a right conjunct. (Contributed by Jeff Hankins, 30-Aug-2009.) |
| Ref | Expression |
|---|---|
| impr.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| impr | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | impr.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) | |
| 2 | 1 | ex 412 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| 3 | 2 | imp32 418 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
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