Definition df-bnj19

Description: Define the following predicate: B is transitive for A and R . (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	df-bnj19	$$⊢TrFo\left(B,A,R\right)\leftrightarrow \forall x\in Bpred\left(x,A,R\right)\subseteq B$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cB	$$classB$$
1		cA	$$classA$$
2		cR	$$classR$$
3	1 0 2	w-bnj19	$$wffTrFo\left(B,A,R\right)$$
4		vx	$$setvarx$$
5	4	cv	$$setvarx$$
6	1 2 5	c-bnj14	$$classpred\left(x,A,R\right)$$
7	6 0	wss	$$wffpred\left(x,A,R\right)\subseteq B$$
8	7 4 0	wral	$$wff\forall x\in Bpred\left(x,A,R\right)\subseteq B$$
9	3 8	wb	$$wff\left(TrFo\left(B,A,R\right)\leftrightarrow \forall x\in Bpred\left(x,A,R\right)\subseteq B\right)$$