Definition df-nel 1585

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 1583	. 2 wff A ∉ B
4	1, 2	wcel 956	. . 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 1639  neleq2 1640  ru 1934  pnfnre 5476  mnfnre 5477  ltxrltt 5480  renepnft 5518  renemnft 5519  xrltnrt 5522  pnfnltt 5527  nltmnft 5528  sqr2irr 6667  nthruc 6684  eirr 7343

Copyright terms: Public domain