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Metamath Proof Explorer

Theorem bnj257

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

		Ref	Expression
	Assertion	bnj257	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land ψ \land θ \land χ)$

Step	Hyp	Ref	Expression
1		ancom	$⊢ (χ \land θ) \leftrightarrow (θ \land χ)$
2	1	anbi2i	$⊢ ((φ \land ψ) \land (χ \land θ)) \leftrightarrow ((φ \land ψ) \land (θ \land χ))$
3		bnj256	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow ((φ \land ψ) \land (χ \land θ))$
4		bnj256	$⊢ (φ \land ψ \land θ \land χ) \leftrightarrow ((φ \land ψ) \land (θ \land χ))$
5	2 3 4	3bitr4i	$⊢ (φ \land ψ \land χ \land θ) \leftrightarrow (φ \land ψ \land θ \land χ)$