Metamath Proof Explorer

Theorem bnj422

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	bnj422	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (χ \land θ \land φ \land ψ)$

Proof

Step	Hyp	Ref	Expression
1		bnj345	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (θ \land φ \land ψ \land χ)$
2		bnj345	$⊢ (θ \land φ \land ψ \land χ) \leftrightarrow (χ \land θ \land φ \land ψ)$
3	1 2	bitri	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (χ \land θ \land φ \land ψ)$