Metamath Proof Explorer


Theorem mresspw

Description: A Moore collection is a subset of the power of the base set; each closed subset of the system is actually a subset of the base. (Contributed by Stefan O'Rear, 30-Jan-2015)

Ref Expression
Assertion mresspw CMooreXC𝒫X

Proof

Step Hyp Ref Expression
1 ismre CMooreXC𝒫XXCs𝒫CssC
2 1 simp1bi CMooreXC𝒫X