Theorem simp22

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011)

	Ref	Expression
Assertion	simp22	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		simp2	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜒 )
2	1	3ad2ant2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ) → 𝜒 )