Theorem neleq2 2797

Description: Equality theorem for negated membership. (Contributed by NM, 20-Nov-1994.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)

Assertion

Ref	Expression
neleq2

Proof of Theorem neleq2

Step	Hyp	Ref	Expression
1		eqidd 2458	. 2
2		id 22	. 2
3	1, 2	neleq12d 2794	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e/wnel 2653

This theorem is referenced by:  neleq12dOLD  2799  noinfep  8097  isfbas  20330  nbgra0nb  24429  cusgrares  24472  frgrawopreglem4  25047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-nel 2655