Definition df-nel 2204

Description: Define negated membership. (Contributed by NM, 7-Aug-1994.)

Assertion

Ref	Expression
df-nel	|- (A e/ B <-> -. A e. B)

Detailed syntax breakdown of Definition df-nel

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	wnel 2202	. 2 wff A e/ B
4	1, 2	wcel 1390	. . 3 wff A e. B
5	4	wn 3	. 2 wff -. A e. B
6	3, 5	wb 98	1 wff (A e/ B <-> -. A e. B)

This definition is referenced by:  neli  2293  nelir  2294  neleq1  2295  neleq2  2296  nfnel  2298  nfneld  2299  ru  2757  sbcnel12g  2861  raldifb  3077  pwnss  3903  ruALT  4229  fiprc  6228  0mnnnnn0  7990  rennim  9211  bdnel  9309