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Theorem eleqtrri 2110
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eleqtrr.1
eleqtrr.2  C
Assertion
Ref Expression
eleqtrri  C

Proof of Theorem eleqtrri
StepHypRef Expression
1 eleqtrr.1 . 2
2 eleqtrr.2 . . 3  C
32eqcomi 2041 . 2  C
41, 3eleqtri 2109 1  C
Colors of variables: wff set class
Syntax hints:   wceq 1242   wcel 1390
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  3eltr4i  2116  opi1  3960  opi2  3961  ordpwsucexmid  4246  peano1  4260  acexmidlemcase  5450  acexmidlem2  5452  1lt2pi  6324  prarloclemarch2  6402  prarloclemlt  6475  prarloclemcalc  6484  pnfxr  8442  mnfxr  8444
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