Definition df-nel 2520

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

Assertion

Ref	Expression
df-nel	⊢ (A ∉ B ↔ ¬ A ∈ 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 2518	. 2 wff A ∉ B
4	1, 2	wcel 1710	. . 3 wff A ∈ B
5	4	wn 3	. 2 wff ¬ A ∈ B
6	3, 5	wb 176	1 wff (A ∉ B ↔ ¬ A ∈ B)

This definition is referenced by:  neleq1  2608  neleq2  2609  nfnel  2612  nfneld  2614  ru  3046  sbcnel12g  3154  epprc  5828