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