Metamath Proof Explorer

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	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (χ \land φ \land ψ \land θ)$

Proof

Step	Hyp	Ref	Expression
1		bnj290	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land χ \land θ \land ψ)$
2		bnj257	$⊢ (φ \land χ \land θ \land ψ) \leftrightarrow (φ \land χ \land ψ \land θ)$
3		bnj312	$⊢ (φ \land χ \land ψ \land θ) \leftrightarrow (χ \land φ \land ψ \land θ)$
4	1 2 3	3bitri	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (χ \land φ \land ψ \land θ)$