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Theorem neleqtrd 2569
 Description: If a class is not an element of another class, it is also not an element of an equal class. Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
neleqtrd.1
neleqtrd.2
Assertion
Ref Expression
neleqtrd

Proof of Theorem neleqtrd
StepHypRef Expression
1 neleqtrd.1 . 2
2 neleqtrd.2 . . 3
32eleq2d 2527 . 2
41, 3mtbid 300 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  =wceq 1395  e.wcel 1818 This theorem is referenced by:  neleqtrrd  2570  smoord  7055  r1tskina  9181  mreexexlem2d  15042  opptgdim2  24117  ofccat  28497  stoweidlem26  31808  fourierdlem60  31949  fourierdlem61  31950  dochnel  37120 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-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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