Theorem simp31l

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

	Ref	Expression
Assertion	simp31l	⊢ ( ( 𝜏 ∧ 𝜂 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simp1l	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) → 𝜑 )
2	1	3ad2ant3	⊢ ( ( 𝜏 ∧ 𝜂 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) ) → 𝜑 )