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Metamath Proof Explorer
Description: An importation inference. (Contributed by NM, 26-Apr-1994) (Proof
shortened by Wolf Lammen, 19-Jul-2021)
|
|
Ref |
Expression |
|
Hypothesis |
imp4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
|
Assertion |
imp4a |
⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
imp4.1 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
| 2 |
1
|
imp4b |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) |
| 3 |
2
|
ex |
⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) ) |