Definition df-bdc 15487

Description: Define a bounded class as one such that membership in this class is a bounded formula. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
df-bdc	|- (BOUNDED A <-> A. xBOUNDED x e. A )

Distinct variable group:   x, A

Detailed syntax breakdown of Definition df-bdc

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	wbdc 15486	. 2 wff BOUNDED A
3		vx	. . . . . 6 setvar x
4	3	cv 1363	. . . . 5 class x
5	4, 1	wcel 2167	. . . 4 wff x e. A
6	5	wbd 15458	. . 3 wff BOUNDED x e. A
7	6, 3	wal 1362	. 2 wff A. xBOUNDED x e. A
8	2, 7	wb 105	1 wff (BOUNDED A <-> A. xBOUNDED x e. A )

This definition is referenced by:  bdceq  15488  bdel  15491  bdelir  15493