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Theorem 3eltr4d 2118
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr4d.1
3eltr4d.2  C
3eltr4d.3  D
Assertion
Ref Expression
3eltr4d  C  D

Proof of Theorem 3eltr4d
StepHypRef Expression
1 3eltr4d.2 . 2  C
2 3eltr4d.1 . . 3
3 3eltr4d.3 . . 3  D
42, 3eleqtrrd 2114 . 2  D
51, 4eqeltrd 2111 1  C  D
Colors of variables: wff set class
Syntax hints:   wi 4   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:  ovmpt2dxf  5568  nnaordi  6017  iccf1o  8642
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