Theorem snsspr1

Description: A singleton is a subset of an unordered pair containing its member. (Contributed by NM, 27-Aug-2004)

	Ref	Expression
Assertion	snsspr1	⊢ { 𝐴 } ⊆ { 𝐴 , 𝐵 }

Proof

Step	Hyp	Ref	Expression
1		ssun1	⊢ { 𝐴 } ⊆ ( { 𝐴 } ∪ { 𝐵 } )
2		df-pr	⊢ { 𝐴 , 𝐵 } = ( { 𝐴 } ∪ { 𝐵 } )
3	1 2	sseqtrri	⊢ { 𝐴 } ⊆ { 𝐴 , 𝐵 }