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Metamath Proof Explorer
Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006)
(Proof shortened by Wolf Lammen, 21-Jun-2022)
|
|
Ref |
Expression |
|
Hypothesis |
3impia.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) ) |
|
Assertion |
3impia |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
3impia.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) ) |
| 2 |
1
|
expimpd |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ) |
| 3 |
2
|
3impib |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |