Theorem bnj642

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

	Ref	Expression
Assertion	bnj642	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bnj446	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜑 ) )
2	1	simprbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜑 )