Theorem simp31

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

	Ref	Expression
Assertion	simp31	⊢ ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		simp1	⊢ ( ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) → 𝜒 )
2	1	3ad2ant3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜒 )