bnj290

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

		Ref	Expression
	Assertion	bnj290	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land χ \land θ \land ψ)$

Step	Hyp	Ref	Expression
1		3anrot	$⊢ (ψ \land χ \land θ) \leftrightarrow (χ \land θ \land ψ)$
2	1	anbi2i	$⊢ (φ \land (ψ \land χ \land θ)) \leftrightarrow (φ \land (χ \land θ \land ψ))$
3		bnj252	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land (ψ \land χ \land θ))$
4		bnj252	$⊢ (φ \land χ \land θ \land ψ) \leftrightarrow (φ \land (χ \land θ \land ψ))$
5	2 3 4	3bitr4i	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land χ \land θ \land ψ)$

Metamath Proof Explorer