Metamath Proof Explorer


Theorem brrelex2i

Description: The second argument of a binary relation exists. (An artifact of our ordered pair definition.) (Contributed by Mario Carneiro, 26-Apr-2015)

Ref Expression
Hypothesis brrelexi.1 ⊢ Rel ⁡ R
Assertion brrelex2i ⊢ A R B → B ∈ V

Proof

Step Hyp Ref Expression
1 brrelexi.1 ⊢ Rel ⁡ R
2 brrelex2 ⊢ Rel ⁡ R ∧ A R B → B ∈ V
3 1 2 mpan ⊢ A R B → B ∈ V