Metamath Proof Explorer

Theorem snsspr2

Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 2-May-2009)

Ref Expression
Assertion snsspr2 
|- { B } C_ { A , B }

Proof

Step Hyp Ref Expression
1 ssun2 
 |-  { B } C_ ( { A } u. { B } )
2 df-pr 
 |-  { A , B } = ( { A } u. { B } )
3 1 2 sseqtrri 
 |-  { B } C_ { A , B }