Definition df-nel 1580

Description: Define negated membership.

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 1578	. 2 wff A ∉ B
4	1, 2	wcel 955	. . 3 wff A ∈ B
5	4	wn 2	. 2 wff ¬ A ∈ B
6	3, 5	wb 146	1 wff (A ∉ B ↔ ¬ A ∈ B)

This definition is referenced by:  neleq1 1634  neleq2 1635  ru 1928  pnfnre 5468  mnfnre 5469  ltxrltt 5472  renepnft 5510  renemnft 5511  xrltnrt 5514  pnfnltt 5519  nltmnft 5520  sqr2irr 6659  nthruc 6676  eirr 7335

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