Metamath Proof Explorer
Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011)
(Proof modification is discouraged.) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
e03an.1 |
⊢ 𝜑 |
|
|
e03an.2 |
⊢ ( 𝜓 , 𝜒 , 𝜃 ▶ 𝜏 ) |
|
|
e03an.3 |
⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 ) |
|
Assertion |
e03an |
⊢ ( 𝜓 , 𝜒 , 𝜃 ▶ 𝜂 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
e03an.1 |
⊢ 𝜑 |
2 |
|
e03an.2 |
⊢ ( 𝜓 , 𝜒 , 𝜃 ▶ 𝜏 ) |
3 |
|
e03an.3 |
⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 ) |
4 |
3
|
ex |
⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) ) |
5 |
1 2 4
|
e03 |
⊢ ( 𝜓 , 𝜒 , 𝜃 ▶ 𝜂 ) |