Theorem tpid3

Description: One of the three elements of an unordered triple. (Contributed by NM, 7-Apr-1994) (Proof shortened by Andrew Salmon, 29-Jun-2011) (Proof shortened by JJ, 30-Apr-2021)

	Ref	Expression
Hypothesis	tpid3.1	⊢ 𝐶 ∈ V
Assertion	tpid3	⊢ 𝐶 ∈ { 𝐴 , 𝐵 , 𝐶 }

Proof

Step	Hyp	Ref	Expression
1		tpid3.1	⊢ 𝐶 ∈ V
2		tpid3g	⊢ ( 𝐶 ∈ V → 𝐶 ∈ { 𝐴 , 𝐵 , 𝐶 } )
3	1 2	ax-mp	⊢ 𝐶 ∈ { 𝐴 , 𝐵 , 𝐶 }