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Theorem 3eltr4i 2517
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr4.1  |-  A  e.  B
3eltr4.2  |-  C  =  A
3eltr4.3  |-  D  =  B
Assertion
Ref Expression
3eltr4i  |-  C  e.  D

Proof of Theorem 3eltr4i
StepHypRef Expression
1 3eltr4.2 . 2  |-  C  =  A
2 3eltr4.1 . . 3  |-  A  e.  B
3 3eltr4.3 . . 3  |-  D  =  B
42, 3eleqtrri 2511 . 2  |-  A  e.  D
51, 4eqeltri 2508 1  |-  C  e.  D
Colors of variables: wff set class
Syntax hints:    = wceq 1653    e. wcel 1726
This theorem is referenced by:  oancom  7609  0r  8960  1sr  8961  m1r  8962  lmxrge0  24342  brsigarn  24543  sinccvglem  25114
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2431  df-clel 2434
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