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Theorem eleqtrri 2095
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eleqtrr.1 A B
eleqtrr.2 𝐶 = B
Assertion
Ref Expression
eleqtrri A 𝐶

Proof of Theorem eleqtrri
StepHypRef Expression
1 eleqtrr.1 . 2 A B
2 eleqtrr.2 . . 3 𝐶 = B
32eqcomi 2026 . 2 B = 𝐶
41, 3eleqtri 2094 1 A 𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1228   wcel 1374
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-cleq 2015  df-clel 2018
This theorem is referenced by:  3eltr4i  2101  opi1  3943  opi2  3944  ordpwsucexmid  4230  peano1  4244  acexmidlemcase  5431  acexmidlem2  5433  1lt2pi  6200  prarloclemarch2  6276  prarloclemlt  6347  prarloclemcalc  6356
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