Theorem bnj334

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj334	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj290	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) )
2		bnj257	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜃 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃 ) )
3		bnj312	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) )
4	1 2 3	3bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( 𝜒 ∧ 𝜑 ∧ 𝜓 ∧ 𝜃 ) )