Metamath Proof Explorer
Description: Deduction adding 10 conjuncts to antecedent. (Contributed by Mario
Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)
|
|
Ref |
Expression |
|
Hypothesis |
ad2ant.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
ad10antr |
⊢ ( ( ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) ∧ 𝜅 ) → 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ad2ant.1 |
⊢ ( 𝜑 → 𝜓 ) |
2 |
1
|
adantr |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 ) |
3 |
2
|
ad9antr |
⊢ ( ( ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) ∧ 𝜅 ) → 𝜓 ) |