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
|- ( 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 ) )