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Theorem 3eltr4i 2561
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 2547 . 2  |-  A  e.  D
51, 4eqeltri 2544 1  |-  C  e.  D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1374    e. wcel 1762
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-cleq 2452  df-clel 2455
This theorem is referenced by:  oancom  8057  0r  9446  1sr  9447  m1r  9448  lmxrge0  27556  brsigarn  27781  sinccvglem  28499  bj-minftyccb  33575
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