Definition df-bdc 13723

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 ↔ ∀𝑥BOUNDED 𝑥 ∈ 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 13722	. 2 wff BOUNDED 𝐴
3		vx	. . . . . 6 setvar 𝑥
4	3	cv 1342	. . . . 5 class 𝑥
5	4, 1	wcel 2136	. . . 4 wff 𝑥 ∈ 𝐴
6	5	wbd 13694	. . 3 wff BOUNDED 𝑥 ∈ 𝐴
7	6, 3	wal 1341	. 2 wff ∀𝑥BOUNDED 𝑥 ∈ 𝐴
8	2, 7	wb 104	1 wff (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥 ∈ 𝐴)

This definition is referenced by:  bdceq  13724  bdel  13727  bdelir  13729