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| Mirrors > Home > MPE Home > Th. List > 3exp | Structured version Visualization version GIF version | ||
| Description: Exportation inference. (Contributed by NM, 30-May-1994.) (Proof shortened by Wolf Lammen, 22-Jun-2022.) |
| Ref | Expression |
|---|---|
| 3exp.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| 3exp | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3exp.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
| 2 | 1 | 3expa 1119 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
| 3 | 2 | exp31 419 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
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