Metamath Proof Explorer

Definition df-bnj13

Description: Define the following predicate: R is set-like on A . (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion df-bnj13 ⊢ R Se A ↔ ∀ x ∈ A pred x A R ∈ V

Detailed syntax breakdown

Step Hyp Ref Expression
0 cR class R
1 cA class A
2 1 0 w-bnj13 wff R Se A
3 vx setvar x
4 3 cv setvar x
5 1 0 4 c-bnj14 class pred x A R
6 cvv class V
7 5 6 wcel wff pred x A R ∈ V
8 7 3 1 wral wff ∀ x ∈ A pred x A R ∈ V
9 2 8 wb wff R Se A ↔ ∀ x ∈ A pred x A R ∈ V