Metamath Proof Explorer

Theorem bnj248

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

		Ref	Expression
	Assertion	bnj248	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (((φ \land ψ) \land χ) \land θ)$

Step	Hyp	Ref	Expression
1		df-bnj17	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((φ \land ψ \land χ) \land θ)$
2		df-3an	$⊢ (φ \land ψ \land χ) \leftrightarrow ((φ \land ψ) \land χ)$
3	2	anbi1i	$⊢ ((φ \land ψ \land χ) \land θ) \leftrightarrow (((φ \land ψ) \land χ) \land θ)$
4	1 3	bitri	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (((φ \land ψ) \land χ) \land θ)$