Metamath Proof Explorer
Description: Elimination rule similar to mp4an , except with a left-nested
conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017)
|
|
Ref |
Expression |
|
Hypotheses |
eel0000.1 |
⊢ 𝜑 |
|
|
eel0000.2 |
⊢ 𝜓 |
|
|
eel0000.3 |
⊢ 𝜒 |
|
|
eel0000.4 |
⊢ 𝜃 |
|
|
eel0000.5 |
⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |
|
Assertion |
eel0000 |
⊢ 𝜏 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
eel0000.1 |
⊢ 𝜑 |
2 |
|
eel0000.2 |
⊢ 𝜓 |
3 |
|
eel0000.3 |
⊢ 𝜒 |
4 |
|
eel0000.4 |
⊢ 𝜃 |
5 |
|
eel0000.5 |
⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |
6 |
5
|
exp41 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) ) |
7 |
1 2 6
|
mp2 |
⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) ) |
8 |
3 4 7
|
mp2 |
⊢ 𝜏 |