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 ( B , A , R ) <-> A. x e. B _pred ( x , A , R ) C_ B )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cB	|- B
1		cA	|- A
2		cR	|- R
3	1 0 2	w-bnj19	|- _TrFo ( B , A , R )
4		vx	|- x
5	4	cv	|- x
6	1 2 5	c-bnj14	|- _pred ( x , A , R )
7	6 0	wss	|- _pred ( x , A , R ) C_ B
8	7 4 0	wral	|- A. x e. B _pred ( x , A , R ) C_ B
9	3 8	wb	|- ( _TrFo ( B , A , R ) <-> A. x e. B _pred ( x , A , R ) C_ B )