bnj312

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

		Ref	Expression
	Assertion	bnj312	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (ψ \land φ \land χ \land θ)$

Step	Hyp	Ref	Expression
1		3ancoma	$⊢ (φ \land ψ \land χ) \leftrightarrow (ψ \land φ \land χ)$
2	1	anbi1i	$⊢ ((φ \land ψ \land χ) \land θ) \leftrightarrow ((ψ \land φ \land χ) \land θ)$
3		df-bnj17	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((φ \land ψ \land χ) \land θ)$
4		df-bnj17	$⊢ (ψ \land φ \land χ \land θ) \leftrightarrow ((ψ \land φ \land χ) \land θ)$
5	2 3 4	3bitr4i	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (ψ \land φ \land χ \land θ)$

Metamath Proof Explorer