Metamath Proof Explorer

Theorem 4an31

Description: A rearrangement of conjuncts for a 4-right-nested conjunction. (Contributed by Alan Sare, 30-May-2018)

		Ref	Expression
	Hypothesis	4an31.1	$⊢ (((χ \land ψ) \land φ) \land θ) \to τ$
	Assertion	4an31	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$

Step	Hyp	Ref	Expression
1		4an31.1	$⊢ (((χ \land ψ) \land φ) \land θ) \to τ$
2		an31	$⊢ ((φ \land ψ) \land χ) \leftrightarrow ((χ \land ψ) \land φ)$
3	2 1	sylanb	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$