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Theorem 3eltr3i 2115
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr3.1
3eltr3.2  C
3eltr3.3  D
Assertion
Ref Expression
3eltr3i  C  D

Proof of Theorem 3eltr3i
StepHypRef Expression
1 3eltr3.2 . 2  C
2 3eltr3.1 . . 3
3 3eltr3.3 . . 3  D
42, 3eleqtri 2109 . 2  D
51, 4eqeltrri 2108 1  C  D
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: (None)
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