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Theorem eqneltrrd 2530
 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.)
Hypotheses
Ref Expression
eqneltrrd.1
eqneltrrd.2
Assertion
Ref Expression
eqneltrrd

Proof of Theorem eqneltrrd
StepHypRef Expression
1 eqneltrrd.2 . 2
2 eqneltrrd.1 . . 3
32eleq1d 2502 . 2
41, 3mtbid 292 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1652   wcel 1725 This theorem is referenced by:  bitsf1  12958  lssvancl2  16022  lbsind2  16153  lindfind2  27265  2atjlej  30276  2atnelvolN  30384 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429  df-clel 2432
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