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Mirrors > Home > MPE Home > Th. List > impd | Structured version Visualization version GIF version |
Description: Importation deduction. (Contributed by NM, 31-Mar-1994.) |
Ref | Expression |
---|---|
impd.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
impd | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impd.1 | . . . 4 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | com3l 89 | . . 3 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃))) |
3 | 2 | imp 410 | . 2 ⊢ ((𝜓 ∧ 𝜒) → (𝜑 → 𝜃)) |
4 | 3 | com12 32 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
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