Metamath Proof Explorer


Theorem ssexi

Description: The subset of a set is also a set. (Contributed by NM, 9-Sep-1993)

Ref Expression
Hypotheses ssexi.1
|- B e. _V
ssexi.2
|- A C_ B
Assertion ssexi
|- A e. _V

Proof

Step Hyp Ref Expression
1 ssexi.1
 |-  B e. _V
2 ssexi.2
 |-  A C_ B
3 1 ssex
 |-  ( A C_ B -> A e. _V )
4 2 3 ax-mp
 |-  A e. _V