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	$$⊢RSeA\leftrightarrow \forall x\in Apred\left(x,A,R\right)\in \mathrm{V}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cR	$$classR$$
1		cA	$$classA$$
2	1 0	w-bnj13	$$wffRSeA$$
3		vx	$$setvarx$$
4	3	cv	$$setvarx$$
5	1 0 4	c-bnj14	$$classpred\left(x,A,R\right)$$
6		cvv	$$class\mathrm{V}$$
7	5 6	wcel	$$wffpred\left(x,A,R\right)\in \mathrm{V}$$
8	7 3 1	wral	$$wff\forall x\in Apred\left(x,A,R\right)\in \mathrm{V}$$
9	2 8	wb	$$wff\left(RSeA\leftrightarrow \forall x\in Apred\left(x,A,R\right)\in \mathrm{V}\right)$$