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

Theorem eqeltrri 2424
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqeltrr.1
eqeltrr.2
Assertion
Ref Expression
eqeltrri

Proof of Theorem eqeltrri
StepHypRef Expression
1 eqeltrr.1 . . 3
21eqcomi 2357 . 2
3 eqeltrr.2 . 2
42, 3eqeltri 2423 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:  3eltr3i  2431  vvex  4109  0ex  4110  nnc0suc  4412  nncaddccl  4419  nnsucelrlem1  4424  nndisjeq  4429  preaddccan2lem1  4454  ltfintrilem1  4465  ssfin  4470  ncfinraiselem2  4480  ncfinlowerlem1  4482  tfin0c  4497  evenoddnnnul  4514  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  sfintfinlem1  4531  tfinnnlem1  4533  vfinspss  4551  vfinspclt  4552  vfinncsp  4554  phialllem1  4616  clos1ex  5876  clos1basesuc  5882  mapexi  6003  fnpm  6008  enpw1lem1  6061  nenpw1pwlem1  6084  tc0c  6163  tc1c  6165  2nnc  6167  ce0nn  6180  ce0  6190  leconnnc  6218  nclennlem1  6247  nnltp1clem1  6260  addccan2nclem2  6263  nmembers1lem1  6267  nncdiv3lem2  6274  nnc3n3p1  6276  spacvallem1  6279  nchoicelem4  6290  nchoicelem11  6297  nchoicelem12  6298  nchoicelem16  6302  nchoicelem17  6303  nchoicelem18  6304
  Copyright terms: Public domain W3C validator