Theorem tpex

Description: An unordered triple of classes exists. (Contributed by NM, 10-Apr-1994)

	Ref	Expression
Assertion	tpex	⊢ { 𝐴 , 𝐵 , 𝐶 } ∈ V

Proof

Step	Hyp	Ref	Expression
1		df-tp	⊢ { 𝐴 , 𝐵 , 𝐶 } = ( { 𝐴 , 𝐵 } ∪ { 𝐶 } )
2		prex	⊢ { 𝐴 , 𝐵 } ∈ V
3		snex	⊢ { 𝐶 } ∈ V
4	2 3	unex	⊢ ( { 𝐴 , 𝐵 } ∪ { 𝐶 } ) ∈ V
5	1 4	eqeltri	⊢ { 𝐴 , 𝐵 , 𝐶 } ∈ V