Theorem snsstp3

Description: A singleton is a subset of an unordered triple containing its member. (Contributed by NM, 9-Oct-2013)

	Ref	Expression
Assertion	snsstp3	⊢ { 𝐶 } ⊆ { 𝐴 , 𝐵 , 𝐶 }

Proof

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