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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 ⊆ 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