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

Step	Hyp	Ref	Expression
1		neleqtrd.1	. 2
2		neleqtrd.2	. . 3
3	2	eleq2d 2527	. 2
4	1, 3	mtbid 300	1

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