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	$$⊢\phi \to A\in \mathrm{ACS}\left(X\right)$$
Assertion	acsmred	$$⊢\phi \to A\in \mathrm{Moore}\left(X\right)$$

Proof

Step	Hyp	Ref	Expression
1		acsmred.1	$$⊢\phi \to A\in \mathrm{ACS}\left(X\right)$$
2		acsmre	$$⊢A\in \mathrm{ACS}\left(X\right)\to A\in \mathrm{Moore}\left(X\right)$$
3	1 2	syl	$$⊢\phi \to A\in \mathrm{Moore}\left(X\right)$$