Theorem simp-6l

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

	Ref	Expression
Assertion	simp-6l	⊢ ( ( ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2	1	ad6antr	⊢ ( ( ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) → 𝜑 )