MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  neleq12d Unicode version

Theorem neleq12d 2794
Description: Equality theorem for negated membership. (Contributed by FL, 10-Aug-2016.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypotheses
Ref Expression
neleq12d.1
neleq12d.2
Assertion
Ref Expression
neleq12d

Proof of Theorem neleq12d
StepHypRef Expression
1 neleq12d.1 . . . 4
2 neleq12d.2 . . . 4
31, 2eleq12d 2539 . . 3
43notbid 294 . 2
5 df-nel 2655 . 2
6 df-nel 2655 . 2
74, 5, 63bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  e/wnel 2653
This theorem is referenced by:  neleq1  2795  neleq2  2797  usgrares1  24410  nbgranself  24434  nbgrassovt  24435  frgrancvvdeqlem2  25031
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
  Copyright terms: Public domain W3C validator