NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  eleqtrri Unicode version

Theorem eleqtrri 2426
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eleqtrr.1
eleqtrr.2
Assertion
Ref Expression
eleqtrri

Proof of Theorem eleqtrri
StepHypRef Expression
1 eleqtrr.1 . 2
2 eleqtrr.2 . . 3
32eqcomi 2357 . 2
41, 3eleqtri 2425 1
Colors of variables: wff setvar class
Syntax hints:   wceq 1642   wcel 1710
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349
This theorem is referenced by:  3eltr4i  2432  0cnsuc  4401  0ceven  4505  ncvspfin  4538  ce0  6190  cet  6234  nmembers1  6271
  Copyright terms: Public domain W3C validator