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Theorem eqeltrri 2108
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqeltrr.1 A = B
eqeltrr.2 A 𝐶
Assertion
Ref Expression
eqeltrri B 𝐶

Proof of Theorem eqeltrri
StepHypRef Expression
1 eqeltrr.1 . . 3 A = B
21eqcomi 2041 . 2 B = A
3 eqeltrr.2 . 2 A 𝐶
42, 3eqeltri 2107 1 B 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:  3eltr3i  2115  p0ex  3930  epse  4064  unex  4142  ordtri2orexmid  4211  onsucsssucexmid  4212  ordsoexmid  4240  nnregexmid  4285  abrexex  5686  opabex3  5691  abrexex2  5693  abexssex  5694  abexex  5695  oprabrexex2  5699  tfr0  5878  1lt2pi  6324  prarloclemarch2  6402  prarloclemlt  6475  0cn  6797  resubcli  7050  0reALT  7084  numsucc  8149  nummac  8155  qreccl  8331  unirnioo  8592  bj-unex  9350
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