Theorem bnj446

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

	Ref	Expression
Assertion	bnj446	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj345	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑 ) ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
2		df-bnj17	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜑 ) ↔ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜑 ) )
3	1 2	bitr3i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜑 ) )