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Theorem neleqtrrd 2136
 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
neleqtrrd.1
neleqtrrd.2
Assertion
Ref Expression
neleqtrrd

Proof of Theorem neleqtrrd
StepHypRef Expression
1 neleqtrrd.1 . 2
2 neleqtrrd.2 . . 3
32eleq2d 2107 . 2
41, 3mtbird 598 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1243   wcel 1393 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036 This theorem is referenced by: (None)
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