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Theorem 3eltr4i 2520
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 2514 . 2  |-  A  e.  D
51, 4eqeltri 2511 1  |-  C  e.  D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    e. wcel 1756
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792  ax-ext 2422
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1587  df-cleq 2434  df-clel 2437
This theorem is referenced by:  oancom  7855  0r  9245  1sr  9246  m1r  9247  lmxrge0  26380  brsigarn  26596  sinccvglem  27315  bj-minftyccb  32545
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