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Metamath Proof Explorer

Theorem 3anan32

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

		Ref	Expression
	Assertion	3anan32	$⊢ (φ \land ψ \land χ) \leftrightarrow ((φ \land χ) \land ψ)$

Step	Hyp	Ref	Expression
1		df-3an	$⊢ (φ \land ψ \land χ) \leftrightarrow ((φ \land ψ) \land χ)$
2		an32	$⊢ ((φ \land ψ) \land χ) \leftrightarrow ((φ \land χ) \land ψ)$
3	1 2	bitri	$⊢ (φ \land ψ \land χ) \leftrightarrow ((φ \land χ) \land ψ)$