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Metamath Proof Explorer

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 }