Metamath Proof Explorer


Theorem mrcssvd

Description: The Moore closure of a set is a subset of the base. Deduction form of mrcssv . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypotheses mrcssd.1 φAMooreX
mrcssd.2 N=mrClsA
Assertion mrcssvd φNBX

Proof

Step Hyp Ref Expression
1 mrcssd.1 φAMooreX
2 mrcssd.2 N=mrClsA
3 2 mrcssv AMooreXNBX
4 1 3 syl φNBX