Metamath Proof Explorer
Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011)
(Proof modification is discouraged.) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
e10an.1 |
⊢ ( 𝜑 ▶ 𝜓 ) |
|
|
e10an.2 |
⊢ 𝜒 |
|
|
e10an.3 |
⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
e10an |
⊢ ( 𝜑 ▶ 𝜃 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
e10an.1 |
⊢ ( 𝜑 ▶ 𝜓 ) |
2 |
|
e10an.2 |
⊢ 𝜒 |
3 |
|
e10an.3 |
⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) |
4 |
3
|
ex |
⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) ) |
5 |
1 2 4
|
e10 |
⊢ ( 𝜑 ▶ 𝜃 ) |