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 → 𝐴 ∈ ( ACS ‘ 𝑋 ) )
Assertion	acsmred	⊢ ( 𝜑 → 𝐴 ∈ ( Moore ‘ 𝑋 ) )

Proof

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