Metamath Proof Explorer
Theorem e3
Description: Meta-connective form of syl8 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
e3.1 |
⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
|
|
e3.2 |
⊢ ( 𝜃 → 𝜏 ) |
|
Assertion |
e3 |
⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
e3.1 |
⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
2 |
|
e3.2 |
⊢ ( 𝜃 → 𝜏 ) |
3 |
2
|
a1i |
⊢ ( 𝜃 → ( 𝜃 → 𝜏 ) ) |
4 |
1 1 3
|
e33 |
⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |