Theorem simpl1

Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Assertion	simpl1	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜑 )
2	1	3ad2antl1	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 )