Metamath Proof Explorer

Theorem bnj432

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

		Ref	Expression
	Assertion	bnj432	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((χ \land θ) \land (φ \land ψ))$

Step	Hyp	Ref	Expression
1		bnj422	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (χ \land θ \land φ \land ψ)$
2		bnj256	$⊢ (χ \land θ \land φ \land ψ) \leftrightarrow ((χ \land θ) \land (φ \land ψ))$
3	1 2	bitri	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((χ \land θ) \land (φ \land ψ))$