Metamath Proof Explorer
Description: Conjunction form of e22 . (Contributed by Alan Sare, 11-Jun-2011)
(Proof modification is discouraged.) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
e22an.1 |
⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
|
|
e22an.2 |
⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
|
|
e22an.3 |
⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) |
|
Assertion |
e22an |
⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
e22an.1 |
⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
2 |
|
e22an.2 |
⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
3 |
|
e22an.3 |
⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) |
4 |
3
|
ex |
⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) ) |
5 |
1 2 4
|
e22 |
⊢ ( 𝜑 , 𝜓 ▶ 𝜏 ) |