Theorem simp12

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

	Ref	Expression
Assertion	simp12	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		simp2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜓 )
2	1	3ad2ant1	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ∧ 𝜏 ) → 𝜓 )