Theorem simp123

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

	Ref	Expression
Assertion	simp123	⊢ ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) ∧ 𝜂 ∧ 𝜁 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		simp23	⊢ ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) → 𝜒 )
2	1	3ad2ant1	⊢ ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜏 ) ∧ 𝜂 ∧ 𝜁 ) → 𝜒 )