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Metamath Proof Explorer

Theorem anasss

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by NM, 15-Nov-2002)

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

Step	Hyp	Ref	Expression
1		anasss.1	$⊢ ((φ \land ψ) \land χ) \to θ$
2	1	exp31	$⊢ φ \to (ψ \to (χ \to θ))$
3	2	imp32	$⊢ (φ \land (ψ \land χ)) \to θ$