Metamath Proof Explorer
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 24-May-2022)
|
|
Ref |
Expression |
|
Assertion |
simp-9r |
⊢ ( ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
id |
⊢ ( 𝜓 → 𝜓 ) |
2 |
1
|
ad9antlr |
⊢ ( ( ( ( ( ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → 𝜓 ) |