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Metamath Proof Explorer
Description: Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995) (Revised to shorten 3imp by Wolf Lammen,
20-Jun-2022.)
|
|
Ref |
Expression |
|
Hypothesis |
3impa.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
3impa |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
3impa.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
| 2 |
|
df-3an |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) |
| 3 |
2 1
|
sylbi |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |