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 } ⊆ { 𝐴 , 𝐵 }

Proof

Step	Hyp	Ref	Expression
1		ssun2	⊢ { 𝐵 } ⊆ ( { 𝐴 } ∪ { 𝐵 } )
2		df-pr	⊢ { 𝐴 , 𝐵 } = ( { 𝐴 } ∪ { 𝐵 } )
3	1 2	sseqtrri	⊢ { 𝐵 } ⊆ { 𝐴 , 𝐵 }