Metamath Proof Explorer


Theorem simp-7l

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 24-May-2022)

Ref Expression
Assertion simp-7l ( ( ( ( ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 id ( 𝜑𝜑 )
2 1 ad7antr ( ( ( ( ( ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) ∧ 𝜎 ) → 𝜑 )