Theorem simp311

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)

	Ref	Expression
Assertion	simp311	⊢ ( ( 𝜂 ∧ 𝜁 ∧ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simp11	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) → 𝜑 )
2	1	3ad2ant3	⊢ ( ( 𝜂 ∧ 𝜁 ∧ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) ) → 𝜑 )