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 ( 𝜑𝐴 ∈ ( ACS ‘ 𝑋 ) )
Assertion acsmred ( 𝜑𝐴 ∈ ( Moore ‘ 𝑋 ) )

Proof

Step Hyp Ref Expression
1 acsmred.1 ( 𝜑𝐴 ∈ ( ACS ‘ 𝑋 ) )
2 acsmre ( 𝐴 ∈ ( ACS ‘ 𝑋 ) → 𝐴 ∈ ( Moore ‘ 𝑋 ) )
3 1 2 syl ( 𝜑𝐴 ∈ ( Moore ‘ 𝑋 ) )