Metamath Proof Explorer

Theorem bnj253

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

		Ref	Expression
	Assertion	bnj253	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((φ \land ψ) \land χ \land θ)$

Step	Hyp	Ref	Expression
1		bnj248	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (((φ \land ψ) \land χ) \land θ)$
2		df-3an	$⊢ ((φ \land ψ) \land χ \land θ) \leftrightarrow (((φ \land ψ) \land χ) \land θ)$
3	1 2	bitr4i	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((φ \land ψ) \land χ \land θ)$