Definition df-nel 1193

Description: Define negated membership.

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 1191	. 2 wff A e/ B
4	1, 2	wcel 1092	. . 3 wff A e. B
5	4	wn 1	. 2 wff -. A e. B
6	3, 5	wb 127	1 wff (A e/ B <-> -. A e. B)

This definition is referenced by:  neleq1 1199  neleq2 1200  ru 1437  sqr2irr 4782  nthruc 4784

metamath.org