Theorem snsstp1

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

	Ref	Expression
Assertion	snsstp1	⊢ { 𝐴 } ⊆ { 𝐴 , 𝐵 , 𝐶 }

Proof

Step	Hyp	Ref	Expression
1		snsspr1	⊢ { 𝐴 } ⊆ { 𝐴 , 𝐵 }
2		ssun1	⊢ { 𝐴 , 𝐵 } ⊆ ( { 𝐴 , 𝐵 } ∪ { 𝐶 } )
3	1 2	sstri	⊢ { 𝐴 } ⊆ ( { 𝐴 , 𝐵 } ∪ { 𝐶 } )
4		df-tp	⊢ { 𝐴 , 𝐵 , 𝐶 } = ( { 𝐴 , 𝐵 } ∪ { 𝐶 } )
5	3 4	sseqtrri	⊢ { 𝐴 } ⊆ { 𝐴 , 𝐵 , 𝐶 }