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∈ABC

Proof

Step Hyp Ref Expression
1 tpid3.1 ⊢C∈V
2 tpid3g ⊢C∈V→C∈ABC
3 1 2 ax-mp ⊢C∈ABC