Metamath Proof Explorer

Theorem bnj446

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

		Ref	Expression
	Assertion	bnj446	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((ψ \land χ \land θ) \land φ)$

Step	Hyp	Ref	Expression
1		bnj345	$⊢ (ψ \land χ \land θ \land φ) \leftrightarrow (φ \land ψ \land χ \land θ)$
2		df-bnj17	$⊢ (ψ \land χ \land θ \land φ) \leftrightarrow ((ψ \land χ \land θ) \land φ)$
3	1 2	bitr3i	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((ψ \land χ \land θ) \land φ)$