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Metamath Proof Explorer

Theorem acsmred

Description: An algebraic closure system is also a Moore system. Deduction form of acsmre . (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Hypothesis	acsmred.1	$⊢ φ \to A \in ACS (X)$
	Assertion	acsmred	$⊢ φ \to A \in Moore (X)$

Step	Hyp	Ref	Expression
1		acsmred.1	$⊢ φ \to A \in ACS (X)$
2		acsmre	$⊢ A \in ACS (X) \to A \in Moore (X)$
3	1 2	syl	$⊢ φ \to A \in Moore (X)$