Theorem simp121

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

	Ref	Expression
Assertion	simp121	⊢ ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) ∧ 𝜂 ∧ 𝜁 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		simp21	⊢ ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) → 𝜑 )
2	1	3ad2ant1	⊢ ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) ∧ 𝜂 ∧ 𝜁 ) → 𝜑 )