Theorem simplll

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009) (Proof shortened by Wolf Lammen, 6-Apr-2022)

	Ref	Expression
Assertion	simplll	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝜑 → 𝜑 )
2	1	ad3antrrr	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 )