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Mirrors > Home > MPE Home > Th. List > expimpd | Structured version Visualization version GIF version |
Description: Exportation followed by a deduction version of importation. (Contributed by NM, 6-Sep-2008.) |
Ref | Expression |
---|---|
expimpd.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Ref | Expression |
---|---|
expimpd | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expimpd.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) | |
2 | 1 | ex 416 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | impd 414 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
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