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Theorem eqneltrrd 2567
Description: If a class is not an element of another class, an equal class is also not an element. Deduction form. (Contributed by David Moews, 1-May-2017.) (Proof shortened by Wolf Lammen, 13-Nov-2019.)
Hypotheses
Ref Expression
eqneltrrd.1
eqneltrrd.2
Assertion
Ref Expression
eqneltrrd

Proof of Theorem eqneltrrd
StepHypRef Expression
1 eqneltrrd.1 . . 3
21eqcomd 2465 . 2
3 eqneltrrd.2 . 2
42, 3eqneltrd 2566 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  =wceq 1395  e.wcel 1818
This theorem is referenced by:  bitsf1  14096  lssvancl2  17592  lbsind2  17727  lindfind2  18853  lmod1zrnlvec  33095  2atjlej  35203  2atnelvolN  35311
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
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