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 ) ) |
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 ) ) |