Theorem nelneq 2574

Description: A way of showing two classes are not equal. (Contributed by NM, 1-Apr-1997.)

Assertion

Ref	Expression
nelneq

Proof of Theorem nelneq

Step	Hyp	Ref	Expression
1		eleq1 2529	. . 3
2	1	biimpcd 224	. 2
3	2	con3dimp 441	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818

This theorem is referenced by:  onfununi  7031  suc11reg  8057  cantnfp1lem3  8120  oemapvali  8124  cantnfp1lem3OLD  8146  mreexmrid  15040  supxrnemnf  27583  xrge0neqmnf  27679  onint1  29914  maxidln0  30442  rencldnfilem  30754  icccncfext  31690

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