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Metamath Proof Explorer
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof
shortened by Wolf Lammen, 24-Jun-2022)
|
|
Ref |
Expression |
|
Assertion |
simpl33 |
⊢ ( ( ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜂 ) → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
simpl3 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜂 ) → 𝜒 ) |
| 2 |
1
|
3ad2antl3 |
⊢ ( ( ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜂 ) → 𝜒 ) |