Theorem simp231

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

	Ref	Expression
Assertion	simp231	⊢ ( ( 𝜂 ∧ ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜁 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simp31	⊢ ( ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) → 𝜑 )
2	1	3ad2ant2	⊢ ( ( 𝜂 ∧ ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜁 ) → 𝜑 )