Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  neleqtrd Structured version   Unicode version

Theorem neleqtrd 2530
 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 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:  smoord  6619  r1tskina  8649  mreexexlem2d  13862  stoweidlem26  27732  dochnel  32118 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 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2428  df-clel 2431
 Copyright terms: Public domain W3C validator