Theorem bnj645

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj645	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		df-bnj17	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) )
2	1	simprbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜃 )