Metamath Proof Explorer

Theorem anandirs

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004)

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

Step	Hyp	Ref	Expression
1		anandirs.1	$⊢ ((φ \land χ) \land (ψ \land χ)) \to τ$
2	1	an4s	$⊢ ((φ \land ψ) \land (χ \land χ)) \to τ$
3	2	anabsan2	$⊢ ((φ \land ψ) \land χ) \to τ$