Metamath Proof Explorer

Theorem simp-4l

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

Ref Expression
Assertion simp-4l ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝜑 → 𝜑 )
2 1 ad4antr ⊢ ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) → 𝜑 )