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	|- ( ph -> A e. ( ACS ` X ) )
Assertion	acsmred	|- ( ph -> A e. ( Moore ` X ) )

Proof

Step	Hyp	Ref	Expression
1		acsmred.1	|- ( ph -> A e. ( ACS ` X ) )
2		acsmre	|- ( A e. ( ACS ` X ) -> A e. ( Moore ` X ) )
3	1 2	syl	|- ( ph -> A e. ( Moore ` X ) )