Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > expdimp | Structured version Visualization version GIF version |
Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008.) |
Ref | Expression |
---|---|
expdimp.1 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
Ref | Expression |
---|---|
expdimp | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expdimp.1 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
2 | 1 | expd 419 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | imp 410 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Copyright terms: Public domain | W3C validator |