Theorem simp2ll

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

	Ref	Expression
Assertion	simp2ll	⊢ ( ( 𝜃 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜏 ) → 𝜑 )

Proof

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